Papers by Young-Sea Huang
Recently, the problem of the infinite spherical well was solved by the group-theoretical metho... more Recently, the problem of the infinite spherical well was solved by the group-theoretical method to resolve all the peculiarities in the currently accepted solution [DOI: 10.13140/RG.2.2.18172.44162 (Researchgate, 2017)]. With a view to further justifying the group-theoretical method, the problem is first studied from the viewpoint of classical mechanics. Then the radial probability densities predicted by classical mechanics are compared with those predicted from solutions of the problem obtained by the group-theoretical method. The comparisons clearly indicate the convergence of predictions of quantum mechanics and classical mechanics in the limit of large eigen-energies. Therefore, the group-theoretical method is justified as the right way to solve the problem of the infinite spherical well.
Reply to the Comments by Mohammad Khorrami and
by Antonio Prados and Carlos A. Plata
An error in the currently accepted solution of the problem of the infinite spherical well is poin... more An error in the currently accepted solution of the problem of the infinite spherical well is pointed out. The problem is then solved by considering the self-adjointness of the Hamiltonian operator. In contrast to the currently accepted solution, the radial probability density for finding
the particle at the center of the spherical well is not necessarily zero, in accordance with the solutions obtained.
the author of the paper [1], claims that there is a mistake in our paper [2] that rectified the c... more the author of the paper [1], claims that there is a mistake in our paper [2] that rectified the currently accepted solution of the infinite spherical well. The root of the mistake is due to an oversimplification of the treatment of the Laplacian operator in terms of the spherical polar coordinates, at the origin. By directly substituting n 0 (kr) in the Schrödinger wave equation,
An error in the currently accepted solution of the problem of the infinite spherical well is poin... more An error in the currently accepted solution of the problem of the infinite spherical well is pointed out. The problem is then solved by considering the self-adjointness of the Hamiltonian operator. In contrast to the currently accepted solution, the radial probability density for finding the particle at the center of the spherical well is not necessarily zero, in accordance with the solutions obtained. The usual way of solving the problem of the infinite spherical well is recapitulated in the following [1–3]. Consider a particle of mass µ being confined in a well of spherically symmetric potential V (r) = 0 , if r ≤ a ∞ , if r > a (1) The time-independent Schrödinger wave equation for the physical system is ˆ H ψ(r) = − 2 2µ 2 ψ(r) + V (r) ψ(r) = E ψ(r). (2) In terms of the spherical coordinates (r, θ, φ), the equation becomes 1 2µ r 2 − 2 ∂ ∂ r (r 2 ∂ ∂ r) + ˆ L 2 ψ + V (r)ψ = E ψ. (3)
We argue that special relativity, instead of quantum theory, should be radically reformulated to ... more We argue that special relativity, instead of quantum theory, should be radically reformulated to resolve inconsistencies between those two theories. A new relativistic transformation recently-proposed renders physical laws form-invariant via transformation of physical quantities, instead of space-time coordinates. This new perspective on relativistic transformation provides an insight into the very meaning of the principle of relativity. The principle of relativity means that the same physical laws hold in all inertial frames, rather than their mathematical formulas are Lorentz-covariant under the Lorentz transformation of space-time coordinates. The space-time concept underlying this new relativistic transformation is Newtonian absolute space and absolute time. With this new perspective, quantum theory becomes compatible with the principle of relativity. A new theory of relativistic quantum mechanics is formulated. The new relativistic quantum mechanics thus obtained maintains the ...
A new relativistic transformation in the velocity space (here named the differential Lorentz tran... more A new relativistic transformation in the velocity space (here named the differential Lorentz transformation) is formulated solely from the principle of relativity and the invariance of the speed of light. The differential Lorentz transformation is via transforming physical quantities, instead of space-time coordinates, to make laws of nature form-invariant. The differential Lorentz transformation may provide a way to resolve the incompatibility of the theory of special relativity and the quantum theory.
The dissertation investigates the interpretation of photoemission from f-electron materials. We a... more The dissertation investigates the interpretation of photoemission from f-electron materials. We also discuss unusual room temperature solid-state reactions in Yb-Cu films that we discovered. We show the importance of considering the entire system as a whole in the photoemission process and that photoemission actually measures the energy difference between total energies of the initial state and the final excited state
Solid State Communications, 1988
ABSTRACT Photoemission measurements of Gd films in the photon energy range 16 to 45 eV indicate t... more ABSTRACT Photoemission measurements of Gd films in the photon energy range 16 to 45 eV indicate that a 5p - 5d intershell interaction results in an enhancement of the 5d emission above the and core level thresholds. This resonant behavior has been previously observed in Sm, Yb, and Lu. A constant kinetic energy feature that appears only above the threshold is tentatively identified as being due to autoionization following the creation of a hole with a locally collapsed 5d- screening orbital as an intermediate step.
Solid State Communications, 1989
Journal of Electron Spectroscopy and Related Phenomena, 1990
ABSTRACT Photoemission measurements of Rh films in the photon energy range 40–120 eV show that th... more ABSTRACT Photoemission measurements of Rh films in the photon energy range 40–120 eV show that the 4p-4d intrashell interaction has a Fano-like resonance. The 4d photoemission intensity goes through a sharp dip in the vicinity of the 4p64dn+hv → 4p54dn+1 threshold followed by a resonant enhancement before decreasing again. All parts of the 4d band show the same resonant behavior in contrast to previous resonant photoemission results. The resonant behavior of Rh is compared with Co which is the 3d analog of Rh.
Canadian Journal of Physics, 2008
Does the form invariance of an equation ∂ α A α = 0 imply that A α is a four-vector? We present a... more Does the form invariance of an equation ∂ α A α = 0 imply that A α is a four-vector? We present a simple example to answer this question, with a view to clarifying the misconception that still exists.
According to the current perception of relativistic mechanics, relativistic force is conceived as... more According to the current perception of relativistic mechanics, relativistic force is conceived as defined by the relativistic equation of motion. The transformation of relativistic force, a consequence of the relativistic equation of motion, is the main cause for Trouton-Noble paradox, Lewis-Tolman paradox and Mansuripur's paradox in special relativity. The relativistic equation of motion, as a physical law, should be capable of direct test by experiments. So far the relativistic equation of motion has not been confirmed experimentally. Thus, the validity of the relativistic equation of motion is called into question. An alternative relativistic equation of motion is introduced to compare with the currently accepted relativistic equation of motion, and illustrate how experimental test should be performed without logical circularity. As inspired by the available modern technology used in ion traps, an experiment is proposed to test these two relativistic equations of motion, for particle's speeds $\sim 10^{-3}\,\, c$, much less than the speed of light $c$
Recently, the problem of the infinite square was reexamined by using the self-adjointness of the... more Recently, the problem of the infinite square was reexamined by using the self-adjointness of the Hamiltonian operator and the momentum operator, instead of postulating boundary conditions. The solutions so obtained are free from those peculiarities in the standard solution of the infinite square well. Also, the solutions provide theoretical justification for the periodic boundary conditions applied to the infinite square well.
Here, the same tact is used to study the problem of the finite square well. Boundary conditions allowed for the finite square well are found by the self-adjointness of the Hamiltonian operator. Solutions for bound states of the finite square well are classified into two kinds: (1) the particle is completely confined inside the well, (2) the particle has possibility to leak out of the well. For the first kind, solutions are those of the infinite square well, as obtained previously, for which their energies are less than the potential of the finite square well. For the second kind, there are infinitely many families of solutions, each of which is characterized by the allowed boundary conditions. The well-known standard solution of the finite square well is just one of these families of solutions.
A new theory of relativity is formulated based upon a novel perspective on the relativistic tran... more A new theory of relativity is formulated based upon a novel perspective on the relativistic transformation, namely a transformation in velocity space, rather than space-time space.
The new theory of relativity is applied to study the simple harmonic oscillation in Newtonian mechanics.
As the total energy of the system approaches to an energy comparable to the rest mass energy, the simple harmonic oscillation is transformed into an anharmonic oscillation. The period of the relativistic anharmonic oscillator increases with the amplitude, in contrast to the simple harmonic oscillation.
As the total energy of the system is increased, the curve of the oscillation, displacement versus time, changes from the sinusoidal wave in simple harmonic oscillation to a nearly triangular wave with the curvature concentrated more and more in the vicinity of the turning points. These relativistic anharmonic phenomena are similar to those predicted by Einstein's special relativity, but with less relativistic effects.
Peculiarities in the standard solution of the infinite square well in quantum mechanics are poin... more Peculiarities in the standard solution of the infinite square well in quantum mechanics are pointed out as originated from the conventional boundary condition --- the continuity of wave functions at boundaries. Then, the problem of the infinite square well is solved by using the self-adjointness of the Hamiltonian operator and the momentum operator. The solutions obtained are free from those peculiarities in the standard solution. Only two possible sets of solutions are allowed for the infinite square well, one corresponding to the periodic boundary conditions, and the other corresponding to the anti-periodic boundary conditions. The results provide theoretical justification for the periodic boundary conditions imposed on the infinite square well which is often treated as the model for spatially confined physical systems, for example, in solid state physics.
Flaws and ambiguities are pointed out upon examining the comment attempting to solve a problem
as... more Flaws and ambiguities are pointed out upon examining the comment attempting to solve a problem
as raised recently — the currently accepted formulation of electromagnetic radiation of an accelerated charge violates the principle of conservation of energy. This problem is not solved by the
comment, due to a misunderstanding in the meaning of the total radiated power crossing a sphere.
An experiment is suggested to determine whether on not the currently accepted formulation is valid.
A novel perspective on relativistic transformation recently-proposed provides an insight into the... more A novel perspective on relativistic transformation recently-proposed provides an insight into the
very meaning of the principle of relativity. With this novel perspective and Bell’s theorem, we
argue that special relativity, instead of quantum theory, should be radically reformulated to resolve
inconsistencies between those two theories. A new theory of relativistic quantum mechanics is
formulated upon this novel perspective. This new relativistic quantum mechanics is free from such
anomalies as the negative probability density, the negative-energy states, Zitterbewegung, and the
Klein paradox deep-rooted in the current relativistic quantum mechanics. Moreover, a remarkable
result is found that a particle can not be confined within an infinite square well of width less than
half of the Compton wavelength. As implications in nuclear physics, there is a lower bound on the
size of atomic nucleus. Neither an electron, nor a positron, can be confined inside the nucleus by
whatever interaction.
Furthermore, with this novel perspective, we argue that the postulates of non-relativistic quantum
statistics fulfill the principle of relativity, as extended to the relativistic realm. A new theory of
relativistic quantum statistics is formulated such that the probability distribution functions are the
same as the well-known Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein distribution functions
in non-relativistic quantum statistics. A relativistic speed distribution of a dilute gas is then derived
by the new relativistic quantum statistics and the new relativistic quantum mechanics. This
relativistic speed distribution reduces to Maxwell speed distribution in the low temperature region.
Yet, this relativistic speed distribution differs remarkably from J¨uttner speed distribution in the
high temperature region. Also, thermal properties of a dilute gas are studied by the new relativistic
quantum statistics.
Based on the invariance of the phase of waves, plane waves were shown to propagate with negative
... more Based on the invariance of the phase of waves, plane waves were shown to propagate with negative
frequencies in a medium which moves at ’superluminal’ speed opposite to the propagation direction
of the plane waves. The validity of the invariance of the phase of plane waves was then called into
question. A radical change of the conventional concept of plane waves is recently proposed to solve
the problem of negative frequency of waves.We will explicitly point out flaws in that proposal. Thus,
the validity of the invariance of the phase of plane waves remains questionable.
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Papers by Young-Sea Huang
the particle at the center of the spherical well is not necessarily zero, in accordance with the solutions obtained.
Here, the same tact is used to study the problem of the finite square well. Boundary conditions allowed for the finite square well are found by the self-adjointness of the Hamiltonian operator. Solutions for bound states of the finite square well are classified into two kinds: (1) the particle is completely confined inside the well, (2) the particle has possibility to leak out of the well. For the first kind, solutions are those of the infinite square well, as obtained previously, for which their energies are less than the potential of the finite square well. For the second kind, there are infinitely many families of solutions, each of which is characterized by the allowed boundary conditions. The well-known standard solution of the finite square well is just one of these families of solutions.
The new theory of relativity is applied to study the simple harmonic oscillation in Newtonian mechanics.
As the total energy of the system approaches to an energy comparable to the rest mass energy, the simple harmonic oscillation is transformed into an anharmonic oscillation. The period of the relativistic anharmonic oscillator increases with the amplitude, in contrast to the simple harmonic oscillation.
As the total energy of the system is increased, the curve of the oscillation, displacement versus time, changes from the sinusoidal wave in simple harmonic oscillation to a nearly triangular wave with the curvature concentrated more and more in the vicinity of the turning points. These relativistic anharmonic phenomena are similar to those predicted by Einstein's special relativity, but with less relativistic effects.
as raised recently — the currently accepted formulation of electromagnetic radiation of an accelerated charge violates the principle of conservation of energy. This problem is not solved by the
comment, due to a misunderstanding in the meaning of the total radiated power crossing a sphere.
An experiment is suggested to determine whether on not the currently accepted formulation is valid.
very meaning of the principle of relativity. With this novel perspective and Bell’s theorem, we
argue that special relativity, instead of quantum theory, should be radically reformulated to resolve
inconsistencies between those two theories. A new theory of relativistic quantum mechanics is
formulated upon this novel perspective. This new relativistic quantum mechanics is free from such
anomalies as the negative probability density, the negative-energy states, Zitterbewegung, and the
Klein paradox deep-rooted in the current relativistic quantum mechanics. Moreover, a remarkable
result is found that a particle can not be confined within an infinite square well of width less than
half of the Compton wavelength. As implications in nuclear physics, there is a lower bound on the
size of atomic nucleus. Neither an electron, nor a positron, can be confined inside the nucleus by
whatever interaction.
Furthermore, with this novel perspective, we argue that the postulates of non-relativistic quantum
statistics fulfill the principle of relativity, as extended to the relativistic realm. A new theory of
relativistic quantum statistics is formulated such that the probability distribution functions are the
same as the well-known Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein distribution functions
in non-relativistic quantum statistics. A relativistic speed distribution of a dilute gas is then derived
by the new relativistic quantum statistics and the new relativistic quantum mechanics. This
relativistic speed distribution reduces to Maxwell speed distribution in the low temperature region.
Yet, this relativistic speed distribution differs remarkably from J¨uttner speed distribution in the
high temperature region. Also, thermal properties of a dilute gas are studied by the new relativistic
quantum statistics.
frequencies in a medium which moves at ’superluminal’ speed opposite to the propagation direction
of the plane waves. The validity of the invariance of the phase of plane waves was then called into
question. A radical change of the conventional concept of plane waves is recently proposed to solve
the problem of negative frequency of waves.We will explicitly point out flaws in that proposal. Thus,
the validity of the invariance of the phase of plane waves remains questionable.
the particle at the center of the spherical well is not necessarily zero, in accordance with the solutions obtained.
Here, the same tact is used to study the problem of the finite square well. Boundary conditions allowed for the finite square well are found by the self-adjointness of the Hamiltonian operator. Solutions for bound states of the finite square well are classified into two kinds: (1) the particle is completely confined inside the well, (2) the particle has possibility to leak out of the well. For the first kind, solutions are those of the infinite square well, as obtained previously, for which their energies are less than the potential of the finite square well. For the second kind, there are infinitely many families of solutions, each of which is characterized by the allowed boundary conditions. The well-known standard solution of the finite square well is just one of these families of solutions.
The new theory of relativity is applied to study the simple harmonic oscillation in Newtonian mechanics.
As the total energy of the system approaches to an energy comparable to the rest mass energy, the simple harmonic oscillation is transformed into an anharmonic oscillation. The period of the relativistic anharmonic oscillator increases with the amplitude, in contrast to the simple harmonic oscillation.
As the total energy of the system is increased, the curve of the oscillation, displacement versus time, changes from the sinusoidal wave in simple harmonic oscillation to a nearly triangular wave with the curvature concentrated more and more in the vicinity of the turning points. These relativistic anharmonic phenomena are similar to those predicted by Einstein's special relativity, but with less relativistic effects.
as raised recently — the currently accepted formulation of electromagnetic radiation of an accelerated charge violates the principle of conservation of energy. This problem is not solved by the
comment, due to a misunderstanding in the meaning of the total radiated power crossing a sphere.
An experiment is suggested to determine whether on not the currently accepted formulation is valid.
very meaning of the principle of relativity. With this novel perspective and Bell’s theorem, we
argue that special relativity, instead of quantum theory, should be radically reformulated to resolve
inconsistencies between those two theories. A new theory of relativistic quantum mechanics is
formulated upon this novel perspective. This new relativistic quantum mechanics is free from such
anomalies as the negative probability density, the negative-energy states, Zitterbewegung, and the
Klein paradox deep-rooted in the current relativistic quantum mechanics. Moreover, a remarkable
result is found that a particle can not be confined within an infinite square well of width less than
half of the Compton wavelength. As implications in nuclear physics, there is a lower bound on the
size of atomic nucleus. Neither an electron, nor a positron, can be confined inside the nucleus by
whatever interaction.
Furthermore, with this novel perspective, we argue that the postulates of non-relativistic quantum
statistics fulfill the principle of relativity, as extended to the relativistic realm. A new theory of
relativistic quantum statistics is formulated such that the probability distribution functions are the
same as the well-known Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein distribution functions
in non-relativistic quantum statistics. A relativistic speed distribution of a dilute gas is then derived
by the new relativistic quantum statistics and the new relativistic quantum mechanics. This
relativistic speed distribution reduces to Maxwell speed distribution in the low temperature region.
Yet, this relativistic speed distribution differs remarkably from J¨uttner speed distribution in the
high temperature region. Also, thermal properties of a dilute gas are studied by the new relativistic
quantum statistics.
frequencies in a medium which moves at ’superluminal’ speed opposite to the propagation direction
of the plane waves. The validity of the invariance of the phase of plane waves was then called into
question. A radical change of the conventional concept of plane waves is recently proposed to solve
the problem of negative frequency of waves.We will explicitly point out flaws in that proposal. Thus,
the validity of the invariance of the phase of plane waves remains questionable.