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The propagator of the time-dependent forced harmonic oscillator with constant damping

Bin Kang Cheng

The work of Montroll in deriving the propagator of a time-dependent harmonic oscillator is generalized to obtain the propagator of the time-dependent forced harmonic oscillator with constant damping.

Journal of Mathematical PhysicsJun 1, 198414 citations

The propagator of the time-dependent forced harmonic oscillator with time-dependent damping

Bin Kang Cheng

By using the Caldirola–Kanai Hamiltonian and by applying Feynman polygonal paths, exact evaluation of the propagator of one-dimensional time-dependent forced and damped harmonic oscillator, based on the work of Montroll in deriving the propagator of the harmonic oscillator with time-dependent frequency, is possible. The results are compared with previously found results.

Journal of Mathematical PhysicsJan 1, 198611 citations

Exact Propagator for Darnped Time-Dependent Harmonic Osciilator

Kang Cheng .

mu1 t i p l i e d bya f u n c t i o n o f x', z and T . Here we have de f ined -r = (tr't r ) / n f o r l a t e r convenience. He then c a r r i e r s o u t c a l c u l a t i o n s as T + O ( o r n +a). H i s method has r e c e n t l y been a p p l i e d f o r e v a l u a t i n g t h e propag a t o r o f t ime-dependent fo rced harmonic occ i 1 l a t o r 5 . J n the p resen t work the sane method has been genera l i zed f u r t h e r t o c a l c u l a t e t h e propaga to r o f time-dependent harmonic o s c i l l a t o r w i t h cons tan t damping. I n Sec t ion 2, we a r e a b l e t o t rans fo rm o u r p a t h i n t e g r a l i n t o a f u n c t i o n o f x', x and T. t h e Gaussian i n t e g r a l (1.2) mul t i p l i e d bymu1 t i p l i e d bya f u n c t i o n o f x', z and T . Here we have de f ined -r = (tr't r ) / n f o r l a t e r convenience. He then c a r r i e r s o u t c a l c u l a t i o n s as T + O ( o r n +a). H i s method has r e c e n t l y been a p p l i e d f o r e v a l u a t i n g t h e propag a t o r o f t ime-dependent fo rced harmonic occ i 1 l a t o r 5 . J n the p resen t work the sane method has been genera l i zed f u r t h e r t o c a l c u l a t e t h e propaga to r o f time-dependent harmonic o s c i l l a t o r w i t h cons tan t damping. I n Sec t ion 2, we a r e a b l e t o t rans fo rm o u r p a t h i n t e g r a l i n t o a f u n c t i o n o f x', x and T. t h e Gaussian i n t e g r a l (1.2) mul t i p l i e d by

Jan 1, 19830 citations

Semiclassical approximation and exact evaluation of the propagator for a harmonic oscillator with time-dependent frequency

C. P. Natividade

The propagator for a one-dimensional harmonic oscillator with time-dependent frequency is calculated exactly by the semiclassical approximation method.

American Journal of PhysicsOct 1, 19887 citations

Calculation of the propagator for a time-dependent damped, forced harmonic oscillator using the Schwinger action principle

Luis F. Urrutia, Eduardo Hernández

International Journal of Theoretical PhysicsDec 1, 198418 citations

Exact wavefunction of the time-dependent damped harmonic oscillator with an arbitrary varying mass and with a force quadratic in velocity under the action of an arbitrary time-varying driving force

Gu Zhi-Yu, Qian Shang-Wu

Exact wavefunction of the time-dependent damped harmonic oscillator with an arbitrary varying mass and with a force quadratic in velocity under the action of an arbitrary time-varying driving force, Zhi-Yu Gu, Shang-Wu Qian

Journal of Physics A Mathematical and GeneralJun 7, 19948 citations

The Exact Propagator of Time-Dependent Forced Harmonic Oscillator

Abstract

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The Exact Propagator of Time-Dependent Forced Harmonic Oscillator

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