Lower Bounds for the Energy Levels of Anharmonic Oscillators

1965 ◽  
Vol 43 (10) ◽  
pp. S186-S189 ◽  
Author(s):  
Charles E. Reid
Keyword(s):  
Lower Bounds ◽  
Energy Levels ◽  
Anharmonic Oscillators

Lower bounds for quantum energy levels through statistical mechanics methods

1980 ◽  
Vol 21 (4) ◽  
pp. 834-839 ◽  
Author(s):  
L. Nitti ◽  
M. Pellicoro ◽  
M. Villani
Keyword(s):  
Statistical Mechanics ◽  
Lower Bounds ◽  
Energy Levels ◽  
Quantum Energy

Quantum theory of anharmonic oscillators. II. Energy levels of oscillators with x2α anharmonicity

1976 ◽  
Vol 17 (7) ◽  
pp. 1320-1337 ◽  
Author(s):  
F. T. Hioe ◽  
Don MacMillen ◽  
E. W. Montroll
Keyword(s):  
Quantum Theory ◽  
Energy Levels ◽  
Anharmonic Oscillators

Energy levels of ?x 2k anharmonic oscillators using the quantum normal form

1991 ◽  
Vol 30 (4) ◽  
pp. 487-493 ◽  
Author(s):  
S. Brajamani ◽  
P. S. Mazumdar ◽  
S. K. Chowdhury ◽  
Sukanya Sur
Keyword(s):  
Normal Form ◽  
Energy Levels ◽  
Anharmonic Oscillators

Dirichlet and von Neumann Basis Set for Quantum Mechanical Anharmonic Oscillators

1983 ◽  
Vol 38 (4) ◽  
pp. 473-476 ◽  
Author(s):  
Alejandro M. Mesón ◽  
Francisco M. Fernández ◽  
Eduardo A. Castro
Keyword(s):  
Variational Method ◽  
Harmonic Oscillator ◽  
Lower Bounds ◽  
Neumann Boundary ◽  
Basis Set ◽  
Basis Sets ◽  
Upper And Lower Bounds ◽  
Quantum Mechanical ◽  
Anharmonic Oscillators ◽  
Von Neumann

It is shown that accurate upper and lower bounds to the eigenvalues of anharmonic oscillators can be obtained by means of the Rayleigh-Ritz variational method and two trigonometric basis sets of functions which satisfy Dirichlet and Von Neumann boundary conditions. Numerical results show that the Dirichlet basis set is more appropriate than the harmonic oscillator one for calculating eigenvalues and the value of eigenfunctions at the origin.

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