Spectrum of Quantized Energy for a Lengthening Pendulum

Journal Article · Thu Sep 30 00:00:00 EDT 2010 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3498546· OSTI ID:21428611

Choi, Jeong Ryeol ^[1]; Song, Ji Nny; Hong, Seong Ju ^[2]

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1. School of Electrical Engineering and Computer Science, Kyungpook National University, Daegu 702-701 (Korea, Republic of)
2. Department of Safety Engineering, Chungbuk National University, Cheongju, Chungbuk, 361-763 (Korea, Republic of)

We considered a quantum system of simple pendulum whose length of string is increasing at a steady rate. Since the string length is represented as a time function, this system is described by a time-dependent Hamiltonian. The invariant operator method is very useful in solving the quantum solutions of time-dependent Hamiltonian systems like this. The invariant operator of the system is represented in terms of the lowering operator a(t) and the raising operator a{sup {dagger}}(t). The Schroedinger solutions {psi}{sub n}({theta}, t) whose spectrum is discrete are obtained by means of the invariant operator. The expectation value of the Hamiltonian in the {psi}{sub n}({theta}, t) state is the same as the quantum energy. At first, we considered only {theta}{sup 2} term in the Hamiltonian in order to evaluate the quantized energy. The numerical study for quantum energy correction is also made by considering the angle variable not only up to {theta}{sup 4} term but also up to {theta}{sup 6} term in the Hamiltonian, using the perturbation theory.

• OSTI ID: 21428611
• Journal Information: AIP Conference Proceedings, Vol. 1281, Issue 1; Conference: ICNAAM 2010: International conference of numerical analysis and applied mathematics 2010, Rhodes (Greece), 19-25 Sep 2009; Other Information: DOI: 10.1063/1.3498546; (c) 2010 American Institute of Physics; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
CORRECTIONS
ENERGY SPECTRA
EXPECTATION VALUE
FUNCTIONAL ANALYSIS
HAMILTONIANS
HARMONIC OSCILLATORS
LENGTH
MATHEMATICAL SOLUTIONS
NUMERICAL ANALYSIS
PERTURBATION THEORY
QUANTIZATION
TIME DEPENDENCE
DIMENSIONS
MATHEMATICAL OPERATORS
MATHEMATICS
QUANTUM OPERATORS
SPECTRA