scholarly journals Solution of the Time-Dependent Schrodinger Equation by the Laplace Transform Method

1971 ◽  
Vol 68 (1) ◽  
pp. 76-81 ◽  
Author(s):  
S. H. Lin ◽  
H. Eyring
Keyword(s):  
Schrödinger Equation ◽  
Laplace Transform ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Laplace Transform Method ◽  
Transform Method ◽  
The Laplace Transform

scholarly journals Solution of Schrödinger equation by Laplace transform

1968 ◽  
Vol 8 (3) ◽  
pp. 557-567 ◽  
Author(s):  
M. J. Englefield
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Laplace Transform ◽  
Schrodinger Equation ◽  
Bound State ◽  
Transform Method ◽  
The Laplace Transform ◽  
Scattering Phase ◽  
Straightforward Solution ◽  
The Fourier Transform

Laplace transform techniques for solving differential equations do not seem to have been directly applied to the Schrödinger equation in quantum mechanics. This may be because the Laplace transform of a wave function, in contrast to the Fourier transform, has no direct physical significance. However, this paper will show that scattering phase shifts and bound state energies can be determined from the singularities of the Laplace transform of the wave function. The Laplace transform method can thereby simplify calculations if the potential allows a straightforward solution of the transformed Schrödinger equation. Suitable cases are the Coulomb, oscillator and exponential potentials and the Yamaguchi separable non-local potential.

Timoshenko Beam Dynamics

1971 ◽  
Vol 38 (3) ◽  
pp. 591-594 ◽  
Author(s):  
G. M. Anderson
Keyword(s):  
Laplace Transform ◽  
Timoshenko Beam ◽  
General Problem ◽  
Beam Dynamics ◽  
Time Dependent ◽  
Residue Theorem ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Beam Analysis ◽  
The Laplace Transform

The general problem of Timoshenko beam analysis is solved using the Laplace transform method. Time-dependent boundary and normal loads are considered. It is established that the integrands of the inversion integrals are always single-valued for beams of finite length and modal solutions can always be obtained using the residue theorem.

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