5 research outputs found
PT-symmetric Solutions of Schrodinger Equation with position-dependent mass via Point Canonical Transformation
PT-symmetric solutions of Schrodinger equation are obtained for the Scarf and
generalized harmonic oscillator potentials with the position-dependent mass. A
general point canonical transformation is applied by using a free parameter.
Three different forms of mass distributions are used. A set of the energy
eigenvalues of the bound states and corresponding wave functions for target
potentials are obtained as a function of the free parameter.Comment: 13 page
Quantum fluctuations as deviation from classical dynamics of ensemble of trajectories parameterized by unbiased hidden random variable
A quantization method based on replacement of c-number by c-number
parameterized by an unbiased hidden random variable is developed. In contrast
to canonical quantization, the replacement has straightforward physical
interpretation as statistical modification of classical dynamics of ensemble of
trajectories, and implies a unique operator ordering. We then apply the method
to develop quantum measurement without wave function collapse \'a la pilot-wave
theory.Comment: 14 pages, accepted in Physica
Two-dimensional Schr\"odinger Hamiltonians with Effective Mass in SUSY Approach
The general solution of SUSY intertwining relations of first order for
two-dimensional Schr\"odinger operators with position-dependent (effective)
mass is built in terms of four arbitrary functions. The procedure of separation
of variables for the constructed potentials is demonstrated in general form.
The generalization for intertwining of second order is also considered. The
general solution for a particular form of intertwining operator is found, its
properties - symmetry, irreducibility, separation of variables - are
investigated.Comment: 16 page