Position-dependent mass oscillators and coherent states
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In this paper, the Schrodinger equation for a position-dependent mass quantum system is studied in two ways: first, the interaction is found which must be applied to a mass m(x) in order to supply it with a particular spectrum of energies.Abstract:
The solution of the Schrodinger equation for a position-dependent mass quantum system is studied in two ways. First, the interaction is found which must be applied to a mass m(x) in order to supply it with a particular spectrum of energies. Second, given a specific potential V(x) acting on the mass m(x), the related spectrum is found. The method of solution is applied to a wide class of position-dependent mass oscillators and the corresponding coherent states are constructed. The analytical expressions of such position-dependent mass coherent states preserve the functional structure of the Glauber states.read more
Citations
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Dirac equation for the harmonic scalar and vector potentials and linear plus coulomb-like tensor potential; the SUSY approach
TL;DR: In this paper, a tensor potential is brought into a well-known form of Schrodinger-like problem possessing known solutions via the methodology of supersymmetry (SUSY).
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Position-dependent mass momentum operator and minimal coupling: point canonical transformation and isospectrality
Omar Mustafa,Zeinab Algadhi +1 more
TL;DR: In this paper, the classical and quantum-mechanical correspondence for constant mass settings is used, along with some point canonical transformation, to find the position-dependent mass (PDM) Hamiltonians.
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A position-dependent mass harmonic oscillator and deformed space
TL;DR: In this article, a canonical transformation (x, p)→(x,p,p^q) was proposed to lead a position-dependent mass particle in usual space to another Hamiltonian of a particle with constant mass in a conservative force field of the deformed space.
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On the construction of coherent states of position dependent mass Schrödinger equation endowed with effective potential
TL;DR: In this article, the authors propose an algorithm to construct coherent states for an exactly solvable position dependent mass Schrodinger equation using point canonical transformation method and obtain ground state eigenfunction.
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Dynamical Equations, Invariants and Spectrum Generating Algebras of Mechanical Systems with Position-Dependent Mass
TL;DR: In this paper, it is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass and the time-dependent first integrals of motion are obtained from the factorization of such a constant.
References
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Handbook of Mathematical Functions
Book
Generalized Coherent States and Their Applications
TL;DR: In this paper, the authors define the notion of generalized coherent states and define a generalization of the Coherent State Representation T?(g) of the Heisenberg-Weyl Group.
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Supersymmetry and quantum mechanics
TL;DR: In this article, the authors review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications, including shape invariance and operator transformations, and show that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials.
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Motion of Electrons and Holes in Perturbed Periodic Fields
J. M. Luttinger,Walter Kohn +1 more
TL;DR: In this paper, a new method of developing an "effective-mass" equation for electrons moving in a perturbed periodic structure is discussed, particularly adapted to such problems as arise in connection with impurity states and cyclotron resonance in semiconductors such as Si and Ge.