On the magnetic Hooke-Newton transmutation of electrons

Lin, De-Hone

doi:10.1088/2399-6528/ab3d9a

Cited by 3 publications

(2 citation statements)

References 16 publications

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“…VII, [13], and, e.g., [14][15][16]). The magnetic version of the transmutation with a novel spectrum was discussed in the recent works [11,17,18].…”

Section: The Quadratic Conformal Image Of the Equation For A Charge Imentioning

confidence: 99%

“…In References [11,17,18], the quantum number µ of the transmutation system was taken as µ = m/2 which leads to the solution of the Schrödinger equation in the target space being two-value function, thus violating the single-valuedness condition of the wave function. The single-valuedness solution can be obtained by replacing the quantum number m by 2 m therein.…”

Section: Remarkmentioning

confidence: 99%

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The Magnetic Hooke-Newton Transmutation in Momentum Space

Lin

2021

Symmetry

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The magnetic Hooke-Newton transmutation, which emerges from the transformation design of the quadratic conformal mapping for the system of charged particles moving in the uniform magnetic field, is investigated in the momentum space. It is shown that there are two ways to turn the linear interaction force of the system into the inverse square interaction. The first one, which involves simply applying the mapping to the system, has the spectrum with the Landau levels of even angular momentum quantum number. The second one considers the geometric structure of the mapping as an effective potential which leads us to the transmuted Coulomb system with the novel quantum spectrum. The wave functions of momentum for the bound and scattering states of the transmutation system are given. It is also shown that the effective potential due to the geometric structure can be generalized to a general 2D surface, and the Schrödinger equation of a particle moving on the surface while under the action of the potential can be solved by the form-invariant Schrödinger equation of the free particle. The solution of a particle moving on the hyperbolic surface under the potential is given with the conclusion. The presentation manifests the transformation design of the quantum state, depending mainly on the geometric structure of the representation space, not on the action of the specific potential field. This characteristic makes it possible for us to use the geometric structure of different representation spaces to explore some novel behaviors of quantum particles.

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“…VII, [13], and, e.g., [14][15][16]). The magnetic version of the transmutation with a novel spectrum was discussed in the recent works [11,17,18].…”

Section: The Quadratic Conformal Image Of the Equation For A Charge Imentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

The Magnetic Hooke-Newton Transmutation in Momentum Space

Lin

2021

Symmetry

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The Conformal Image of the Electron

Lin

2024

Annalen der Physik

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The construction of a transformation image is pivotal to the transformation design method for steering waves around an object. Constructing the conformal images of an electron, however, remains a challenge, primarily due to the complexities involved in realizing the spin structure within the image space. This study proposes a novel solution in this regard of the electron's spin structure on a surface, leveraging on the interactions between the electron and a vector potential. By introducing a scalar potential to facilitate the generation of a conformal metric structure and differential operator in the Dirac equation, it is demonstrated that the conformal image of the electron can indeed be constructed within an appropriate electromagnetic field. Furthermore, an equivalence between the geometric effect of a conformal deformation on the electron and the action of an electromagnetic force is established. Electromagnetic fields are used to generate form‐invariant conformal images of the electron within a plane and on a sphere. These examples help showcase the effectiveness of the currently presented method in realizing the conformal images of the electron in various settings.

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Form-invariant solution to quantum state on the sphere

Lin

2020

J. Phys. Commun.

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This paper investigates the quantum states that emerge from the transformation design of conformal mapping on the two-dimensional sphere. Three results are reported. First, the construction of form-invariant spherical harmonics labelled by the fractional quantum number through a scalar potential interaction is given. Second, the form-invariant equation of the charge-monopole system is studied. Rather than the half-integer classification of the monopole harmonics, the quantization of the monopole harmonics here can be any fractional number specified by the conformal index. The gauge equivalent condition of the vector potentials which result in the invariant equation shows that the monopole field and the quantization condition of the pole strength due to Dirac can be generalized to more general vector fields and values in the conformal space. Finally, we explore the quadratic conformal image of the charged particle coupling to the constant monopole field on the sphere. It is shown that the lowest order approximation of the image is the magnetic Hooke-Newton transmutation.

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On the magnetic Hooke-Newton transmutation of electrons

Cited by 3 publications

References 16 publications

The Magnetic Hooke-Newton Transmutation in Momentum Space

The Magnetic Hooke-Newton Transmutation in Momentum Space

The Conformal Image of the Electron

Form-invariant solution to quantum state on the sphere

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