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

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

Variable scaling method and the Stark effect in the hydrogen atom

1985 ◽  
Vol 63 (9) ◽  
pp. 1212-1214
Author(s):  
R. K. Roychoudhury ◽  
Barnana Roy
Keyword(s):  
Hydrogen Atom ◽  
Stark Effect ◽  
Anharmonic Oscillator ◽  
Laguerre Polynomials ◽  
Numerical Results ◽  
Optimal Solutions ◽  
Matrix Elements ◽  
Scaling Method ◽  
Energy Eigenvalues

By relating the Stark-effect problem in hydrogenlike atoms to that of the spherical anharmonic oscillator, we have found simple formulae for energy eigenvalues for the Stark effect. Matrix elements have been calculated using the properties of Laguerre polynomials, and then the variable scaling method has been used to find optimal solutions. Our numerical results are compared with those of Hioe and Yoo and also with the results obtained by Lanczos.

scholarly journals NEW INSIGHTS CONCERNING DIMENSION EIGHT EFFECTS IN WEAK DECAYS

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 1228-1230
Author(s):  
JOHN F. DONOGHUE
Keyword(s):  
Operator Product Expansion ◽  
Short Distance ◽  
Numerical Estimate ◽  
Dimensional Regularization ◽  
Operator Product ◽  
Higher Dimension ◽  
Matrix Elements ◽  
Weak Decays ◽  
The Matrix ◽  
Weak Operator

Most past work on weak nonleptonic decays has mixed dimensional regularization in the weak operator product expansion with some form of a cutoff regularization in the evaluation of the matrix elements. Even with the usual technique of matching the two schemes, this combination misses physics at short distance which can be described by dimension eight (and higher dimension) operators. I describe some recent work with V. Cirigliano and E. Golowich which clarifies these effects and provides a numerical estimate suggesting that they are important.

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
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