Algebraic approach to the forced anharmonic oscillator

Raphaël Khan, Jialun Zhang, Sheng Ding +1 more

Mojtaba Jafarpour, Davood Afshar

We present a new Lie algebraic method to study the eigenvalues and eigenfunctions of quantum anharmonic oscillators. We consider the Hamiltonians for the simple harmonic and anharmonic oscillator as the two generators of a Lie algebra, whose other generators may be found exactly or up to any order of the parameter involved. Speciflcally, the closed commutator algebra for the quartic anharmonic oscillator is established in a perturbation sense. An element of this Lie group, turning out to be the four-photon operator, transforms the quartic anharmonic oscillator Hamiltonian to the harmonic one in a perturbation sense; thus, facilitating the calculation of the eigenvalues and eigenfunctions of the former.

K. S. Viswanathan

George P. Flessas, K. P. Das

Jialun Zhang, Raphaël Khan, Sheng Ding +1 more

The exact solution to a quantum forced anharmonic oscillator is derived. The equation of motion is solved by using the integral operators and iteration method. As a result, the time development of the displacement and momentum operators of the forced anharmonic oscillator is obtained. These operators are presented as a Laplace and a subsequent inverse Laplace transform of suitable functionals.

Artit Hutem

We consider the time-dependent electrostatic force anharmonic oscillator potential in one-dimension. Here, we derive the existing Heisenberg equations of motion from Newton’s second law. We can be used the time-dependent Hamiltonian operator for the time-dependent electrostatic force anharmonic oscillator system. We use the principal of Wronskian method solve for solution of the expectation value of displacement operator for particle bound in anharmonic oscillator potential system. The behavior of the expectation value of displacement operator is wave oscillate depend on the parameter linear frequency, the initial charge, the initial electric, the parameter and .