Perturbation theory for particles in one-dimensional, central- or axial-symmetric fields

1997 ◽  
Vol 112 (1) ◽  
pp. 888-891
Author(s):  
Yu. I. Polyakov
Keyword(s):  
Perturbation Theory ◽  
One Dimensional

One dimensional nonlinear nonsteady state heat conduction I: general solution by perturbation theory

1990 ◽  
Vol 68 (2) ◽  
pp. 198-205 ◽  
Author(s):  
Heinrich Hoff
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Perturbation Theory ◽  
Heat Waves ◽  
Nonlinear Partial Differential Equation ◽  
Homogeneous System ◽  
Nonlinear Field ◽  
One Dimensional ◽  
Future Paper ◽  
Nonsteady State

Taking into account the dependence of the heat capacity and heat conductivity on temperature, one obtains a nonlinear field equation of temperature. This nonlinear partial differential equation is resolved by perturbation theory for the particular case of a homogeneous system. The solution is checked by some criteria of control derived from thermostatics, from steady state transport, and from spatial symmetry. It forms the theoretical framework of nonlinear heat waves to be discussed in a future paper.

STARK HAMILTONIAN WITH UNBOUNDED RANDOM POTENTIALS

1990 ◽  
Vol 02 (04) ◽  
pp. 479-494 ◽  
Author(s):  
PETER D. HISLOP ◽  
SHU NAKAMURA
Keyword(s):  
Perturbation Theory ◽  
Spectral Properties ◽  
Trace Class ◽  
Random Perturbations ◽  
Absolutely Continuous Spectrum ◽  
Random Potentials ◽  
Absolutely Continuous ◽  
One Dimensional ◽  
Accumulation Points ◽  
Mourre Estimate

Spectral properties of one-dimensional Schrödinger operators with unbounded potentials are studied. The main example is the Stark Hamiltonian with unbounded Anderson-type random perturbations. In this case, it is shown that if the perturbation is o(x) then the spectrum is the real line and absolutely continuous except for eigenvalues with no accumulation points. If the perturbation is larger than O(x), then the Hamiltonian has no absolutely continuous spectrum. The methods of proof involve the Mourre estimate and trace-class perturbation theory as recently used by Simon and Spencer.

scholarly journals Two-particle Harmonic Oscillator in a One-dimensional Box

10.14311/1257 ◽  
2010 ◽  
Vol 50 (5) ◽  
Author(s):  
P. Amore ◽  
F. M. Fernández
Keyword(s):  
Perturbation Theory ◽  
Harmonic Oscillator ◽  
Variation Method ◽  
One Dimensional ◽  
Wide Range ◽  
Range Of Values

We study a harmonic molecule confined to a one-dimensional box with impenetrable walls. We explicitly consider the symmetry of the problem for the cases of different and equal masses. We propose suitable variational functions and compare the approximate energies given by the variation method and perturbation theory with accurate numerical ones for a wide range of values of the box length. We analyze the limits of small and large box size.

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