scholarly journals On The Spectral Zeta Function For The Noncommutative Harmonic Oscillator

2007 ◽  
Vol 59 (3) ◽  
pp. 421-432 ◽  
Author(s):  
Takashi Ichinose ◽  
Masato Wakayama
Keyword(s):  
Harmonic Oscillator ◽  
Zeta Function ◽  
Spectral Zeta Function

VACUUM ENERGY IN SPHERICAL DOMAINS: WKB AND UNIFORM ASYMPTOTIC EXPANSIONS

1996 ◽  
Vol 11 (22) ◽  
pp. 4129-4146 ◽  
Author(s):  
AUGUST ROMEO
Keyword(s):  
Zeta Function ◽  
Asymptotic Expansions ◽  
Zero Point ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Point Energy ◽  
Dimensional Dependence ◽  
Spherical Domains ◽  
Spectral Zeta Function ◽  
Uniform Asymptotic Expansions

We evaluate the finite part of the regularized zero-point energy for a massless scalar field confined in the interior of a D-dimensional spherical region. While some insight is offered into the dimensional dependence of the WKB approximations by examining the residues of the spectral-zeta-function poles, a mode-sum technique based on an integral representation of the Bessel spectral zeta function is applied with the help of uniform asymptotic expansions (u.a.e.’s).

The Riemann Zeta Function and the Inverted Harmonic Oscillator

1997 ◽  
Vol 254 (1) ◽  
pp. 25-40 ◽  
Author(s):  
R.K. Bhaduri ◽  
Avinash Khare ◽  
S.M. Reimann ◽  
E.L. Tomusiak
Keyword(s):  
Harmonic Oscillator ◽  
Zeta Function ◽  
Riemann Zeta Function ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

scholarly journals The Casimir effect for thick pistons

2016 ◽  
Vol 31 (06) ◽  
pp. 1650012
Author(s):  
Guglielmo Fucci
Keyword(s):  
Boundary Conditions ◽  
Zeta Function ◽  
Regularization Method ◽  
Casimir Force ◽  
Casimir Effect ◽  
Casimir Energy ◽  
Numerical Results ◽  
Spectral Zeta Function

In this work, we analyze the Casimir energy and force for a thick piston configuration. This study is performed by utilizing the spectral zeta function regularization method. The results we obtain for the Casimir energy and force depend explicitly on the parameters that describe the general self-adjoint boundary conditions imposed. Numerical results for the Casimir force are provided for specific types of boundary conditions and are also compared to the corresponding force on an infinitely thin piston.

scholarly journals The zeta function method and the harmonic oscillator propagator

2001 ◽  
Vol 69 (2) ◽  
pp. 232-235 ◽  
Author(s):  
F. A. Barone ◽  
C. Farina
Keyword(s):  
Harmonic Oscillator ◽  
Zeta Function ◽  
Function Method
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