Abstract
Time-dependent Schrödinger equation (TDSE) is solved numerically to calculate the ground- and first three excited-state energies, expectation values 〈x 2j〉, j=1, 2 …, 6, and probability densities of quantum mechanical multiple-well oscillators. An imaginary-time evolution technique, coupled with the minimization of energy expectation value to reach a global minimum, subject to orthogonality constraint (for excited states) has been employed. Pseudodegeneracy in symmetric, deep multiple-well potentials, probability densities and the effect of an asymmetry parameter on pseudodegeneracy are discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E Magyari, Phys. Lett. A81, 116 (1981)
G P Flessas, J. Phys. A14, L209 (1981)
R Balsa, M Plo, J G Esteve and A F Pacheco, Phys. Rev. D28, 1945 (1983)
R Adhikari, R Dutt and Y P Varshni, Phys. Lett. A14, 1 (1989)
E J Weniger, Phys. Rev. Lett. 77, 2859 (1996)
M Bansal, S Srivastava and Vishwamittar, Phys. Rev. A44, 8012 (1991)
M R M Witwit, J. Phys. A25, 503 (1992)
Mamta and Vishwamittar, Chem. Phys. Lett. 232, 35 (1995)
Yu Zhou, J D Mancini, P F Meier and S P Bowen, Phys. Rev. A51, 3337 (1995)
Y T Liu, K C Ho, C F Lo and K L Liu, Chem. Phys. Lett. 256, 153 (1996)
I A Ivanov, Phys. Rev. A54, 81 (1996)
H Taseli, Int. J. Quantum Chem. 60, 641 (1996)
H Meissner and E O Steinborn, Phys. Rev. A56, 1189 (1997)
R K Agrawal and V S Varma, Phys. Rev. A49, 5089 (1994)
R N Chaudhuri and M Mondal, Phys. Rev. A43, 3241 (1991)
V R Kolagunta, D B Janes, G L Chen, K J Webb and M R Melloch, Appl. Phys. Lett. 69, 374 (1996)
P K Venkatesh, A M Dean, M H Cohen and R W Carr, J. Chem. Phys. 107, 8904 (1997)
L D Landau and L M Lifshitz, Quantum mechanics: Course of theoretical physics (Pergamon Press, Oxford, 1965) vol. 3, p. 57.
R J W Hodgson and Y P Varshni, J. Phys. A22, 61 (1989)
M R M Witwit, J. Comp. Phys. 123, 369 (1996)
W Y Keung, E Kovacs and U P Sukhatme, Phys. Rev. Lett. 60, 41 (1988)
N Gupta, A Wadehra, A K Roy and B M Deb, in Recent advances in atomic and molecular physics edited by R Srivastava (Phoenix Publ., New Delhi, 2001) p. 14
A K Roy, N Gupta and B M Deb, Phys. Rev. A65, 012109 (2002)
A Wadehra, A K Roy and B M Deb, Int. J. Quantum Chem. (In press)
B L Hammond, W A Lester Jr. and P J Reynolds, Monte Carlo methods in ab initio quantum chemistry (World Scientific, Singapore, 1994)
J B Anderson, J. Chem. Phys. 63, 1499 (1975)
J B Anderson, J. Chem. Phys. 65, 412 (1976)
Ph Balcou, A L’Huillier and D Escande, Phys. Rev. A53, 3456 (1996)
B K Dey and B M Deb, J. Chem. Phys. 110, 6229 (1999)
A K Roy, B K Dey and B M Deb, Chem. Phys. Lett. 308, 523 (1999)
G D Smith, Numerical solution of partial differential equations (Oxford University Press, London, 1965)
Author information
Authors and Affiliations
Corresponding author
Additional information
An erratum to this article is available at http://dx.doi.org/10.1007/s12043-002-0159-4.
Rights and permissions
About this article
Cite this article
Gupta, N., Roy, A.K. & Deb, B.M. One-dimensional multiple-well oscillators: A time-dependent quantum mechanical approach. Pramana - J Phys 59, 575–583 (2002). https://doi.org/10.1007/s12043-002-0069-5
Received:
Issue Date:
DOI: https://doi.org/10.1007/s12043-002-0069-5