“…Here again one needs to mention that different versions of nonrelativistic kinetic energy operators (3) exist for the case of effective mass changing with position. There are Gora-Williams, Zhu-Kroemer, von Roos kinetic energy operators [26][27][28] as well as kinetic energy operators based on the contact point transformation method [29][30][31][32] and non-Hermitian PT symmetric kinetic energy operators [33][34][35][36][37][38].…”
Section: Nonrelativistic Harmonic Oscillator Without and With An Exte...mentioning
confidence: 99%
“…Our main goal was to show that the semiconfined quantum harmonic oscillator with position-dependent effective mass is exactly solvable even if it is under an external homogeneous field. We achieved this goal by obtaining analytical expressions of the energy spectrum (31) and normalized wavefunctions (32). In the following section, we are going to discuss some important properties of this model.…”
Section: Nonrelativistic Harmonic Oscillator Without and With An Exte...mentioning
We extend exactly-solvable model of a one-dimensional nonrelativistic canonical semiconfined quantum harmonic oscillator with a mass that varies with position to the case where an external homogeneous field is applied. The problem is still exactly solvable and the analytic expression of the wavefunctions of the stationary states is expressed by means of generalized Laguerre polynomials, too. Unlike the case without any external field, when the energy spectrum completely overlaps with the energy spectrum of the standard nonrelativistic canonical quantum harmonic oscillator, the energy spectrum is now still equidistant but depends on the semiconfinement parameter a. We also compute probabilities of the transitions for the model under the external field and discuss limit cases for the energy spectrum, wavefunctions and probabilities of transitions, when the semiconfinement parameter a goes to infinity.
“…Here again one needs to mention that different versions of nonrelativistic kinetic energy operators (3) exist for the case of effective mass changing with position. There are Gora-Williams, Zhu-Kroemer, von Roos kinetic energy operators [26][27][28] as well as kinetic energy operators based on the contact point transformation method [29][30][31][32] and non-Hermitian PT symmetric kinetic energy operators [33][34][35][36][37][38].…”
Section: Nonrelativistic Harmonic Oscillator Without and With An Exte...mentioning
confidence: 99%
“…Our main goal was to show that the semiconfined quantum harmonic oscillator with position-dependent effective mass is exactly solvable even if it is under an external homogeneous field. We achieved this goal by obtaining analytical expressions of the energy spectrum (31) and normalized wavefunctions (32). In the following section, we are going to discuss some important properties of this model.…”
Section: Nonrelativistic Harmonic Oscillator Without and With An Exte...mentioning
We extend exactly-solvable model of a one-dimensional nonrelativistic canonical semiconfined quantum harmonic oscillator with a mass that varies with position to the case where an external homogeneous field is applied. The problem is still exactly solvable and the analytic expression of the wavefunctions of the stationary states is expressed by means of generalized Laguerre polynomials, too. Unlike the case without any external field, when the energy spectrum completely overlaps with the energy spectrum of the standard nonrelativistic canonical quantum harmonic oscillator, the energy spectrum is now still equidistant but depends on the semiconfinement parameter a. We also compute probabilities of the transitions for the model under the external field and discuss limit cases for the energy spectrum, wavefunctions and probabilities of transitions, when the semiconfinement parameter a goes to infinity.
“…We may now discuss the separability of the PDM Schrödinger equation (14) in the cylindrical coordinates (ρ, φ, z) and under azimuthal symmetrization. By assuming that the field configurations and that the PDM functions are only radially dependent [54,55,[59][60][61] (i,e., m ( − → r ) = M (ρ, φ, z) = g (ρ) ), the wavefunction can be written as…”
Section: Analogous To the Landau-type Quantizationmentioning
confidence: 99%
“…Not only because of its ordering ambiguity associated with the non-unique representation of the kinetic energy operator, but also because of its feasible applicability in many fields of physics. Recent studies on such PDM charged particles in constant magnetic fields [56][57][58][59][60], and position-dependent magnetic fields [61] are carried out (using different interaction potentials). To the best of our knowledge, however, no studies have ever been considered to discuss the quantum mechanical effects on PDM neutral particles possessing an electric quadrupole moment.…”
Section: Introductionmentioning
confidence: 99%
“…In so doing, we use the very recent result suggested by [58,59] for the PDM-minimal-coupling and the PDM-momentum operator. Furthermore, we discuss the possibility of achieving the Landau quantization for such a system, and the separability of the problem in the cylindrical coordinates (ρ, φ, z), under azimuthal symmetrization, by considering that the field configurations and the PDM settings are purely radial dependent as in [54,55,[59][60][61]. In section III, we discuss a Landau levels analog for an electric quadrupole moment interacting with an external magnetic field in the absence of electric field.…”
Analogous to Landau quantization related to a neutral particle possessing an electric quadrupole moment, we generalize such a Landau quantization to include position-dependent mass (PDM) neutral particles. Using cylindrical coordinates, the exact solvability of PDM neutral particles with an electric quadrupole moment moving in electromagnetic fields is reported. The interaction between the electric quadrupole moment of a PDM neutral particle and a magnetic field in the absence of an electric field is analyzed for two different radial cylindrical PDM settings. Next, two particular cases of radial electric fields ( − → E = λ ρ ρ and − → E = λρ 2 ρ) are considered to investigate their influence on the Landau quantization (of this system using the same models of PDM settings). The exact eigenvalues and eigenfunctions for each case are analytically obtained.
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