scholarly journals Energy Eigenvalues of Quantum Anharmonic Oscillators: Exact Expression for the Pure ૃ࢞૛࢓ Oscillators and a Simple Expression for ࢞ૃ ൅ ૛࢞૛࢓ Oscillators

2021 ◽  
Vol 2 (4) ◽  
Keyword(s):  
Exact Expression ◽  
Simple Expression ◽  
Anharmonic Oscillators ◽  
Energy Eigenvalues

Analytical expressions for the energies of anharmonic oscillators

2000 ◽  
Vol 78 (9) ◽  
pp. 845-850
Author(s):  
F M Fernández ◽  
R H Tipping
Keyword(s):  
Perturbation Parameter ◽  
Bound State ◽  
Perturbation Series ◽  
Simple Expression ◽  
Branch Points ◽  
Anharmonic Oscillators ◽  
Large Coupling ◽  
Analytical Behavior ◽  
Schrödinger Perturbation ◽  
Analytical Expressions

We propose a systematic construction of algebraic approximants for the bound-state energies of anharmonic oscillators. The approximants are based on the Rayleigh-Schrödinger perturbation series and take into account the analytical behavior of the energies at large values of the perturbation parameter. A simple expression obtained from a low-order perturbation series compares favorably with alternative approximants. Present approximants converge in the large-coupling limit and are suitable for the calculation of the energy of highly excited states. Moreover, we obtain some branch points of the eigenvalues of the anharmonic oscillator as functions of the coupling constant. PACS No.: 03.65Ge

scholarly journals Anharmonic oscillators in higher dimension: Accurate energy eigenvalues and matrix elements

Pramana ◽  
1989 ◽  
Vol 32 (6) ◽  
pp. 845-845
Author(s):  
V T A Bhargava ◽  
P M Mathews ◽  
M Seetharaman
Keyword(s):  
Higher Dimension ◽  
Matrix Elements ◽  
Anharmonic Oscillators ◽  
Energy Eigenvalues

Simple systematics in the energy eigenvalues of quantum anharmonic oscillators

2007 ◽  
Vol 40 (4) ◽  
pp. 773-784 ◽  
Author(s):  
Ananda Dasgupta ◽  
Dhiranjan Roy ◽  
Ranjan Bhattacharya
Keyword(s):  
Anharmonic Oscillators ◽  
Energy Eigenvalues

An asymptotic expansion for energy eigenvalues of anharmonic oscillators

2013 ◽  
Vol 337 ◽  
pp. 261-277 ◽  
Author(s):  
Philippe Gaudreau ◽  
Richard M. Slevinsky ◽  
Hassan Safouhi
Keyword(s):  
Asymptotic Expansion ◽  
Anharmonic Oscillators ◽  
Energy Eigenvalues

Anharmonic oscillators in higher dimension: Accurate energy eigenvalues and matrix elements

Pramana ◽  
1989 ◽  
Vol 32 (2) ◽  
pp. 107-115 ◽  
Author(s):  
V T A Bhargava ◽  
P M Mathews ◽  
M Seetharaman
Keyword(s):  
Higher Dimension ◽  
Matrix Elements ◽  
Anharmonic Oscillators ◽  
Energy Eigenvalues
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