Path Integral of Time-Dependent Modified Caldirola–Kanai Oscillator

Abstract

We evaluate the propagator, wave function and the uncertainty relation for a time-dependent damped Harmonic oscillator. We also analyze the classical solution of the quantum systems.

Solutions of the Schrödinger Equation with Quantum Mechanical Gravitational Potential Plus Harmonic Oscillator Potential

“…They studied the properties of the partial level density and the total level density numerically for the harmonic oscillator potential well. Also, Ikot et al [15] derived the energy eigen values and the corresponding eigen functions for the two-dimensional harmonic oscillator potential in Cartesian and polar coordinates using the NIkiforov-Uvarov method. Wang et al [16] determined the Virial theorem for a class of quantum nonlinear harmonic oscillators.…”

Bound state solutions ofd-dimensional Schrödinger equation with Eckart potential plus modified deformed Hylleraas potential

“…[14] to study the Schrödinger equation for Eckart plus modified Hylleraas potentials in d dimensions using the Nikiforov-Uvarov method. [15][16][17][18][19][20][21][22][23] The Eckart potential which has been studied by many researchers [8,9] is one of the most important exponential-type potentials in physics and chemical physics whereas the Hylleraas potential can be used to study diatomic molecules. [24,25] Recently, researchers have shown interest in the solutions of the Schrödinger equation in d dimensions, out of the desire to generalize the solution to multi-dimensional space.…”

Approximate solution of Schrodinger equation in D-dimensions for scarf hyperbolic potential using Nikiforov-Uvarov method

“…The one-dimensional Schrodinger equation of any shape invariant potential can be reduced into hypergeometric or confluent hypergeometric type differential equation by suitable variable transformation [12][13][14]. The hypergeometric type differential equation, which is solved using Nikiforov-Uvarov method, is presented as (1) where and are polynomials at most in the second order, and is first order polynomial.…”