Exactly Solvable Models for the Generalized Schrödinger Equation

2012 ◽  
pp. 182-188
Author(s):  
Alina Suzko ◽  
Elena Velicheva
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Generalized Schrödinger Equation ◽  
Exactly Solvable

scholarly journals A class of exactly solvable models for the Schrödinger equation

Open Physics ◽  
2013 ◽  
Vol 11 (8) ◽  
Author(s):  
Charles Downing
Keyword(s):  
Differential Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Mathematical Physics ◽  
Transcendental Equation ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
One Dimensional ◽  
Exactly Solvable ◽  
The One

AbstractWe present a class of confining potentials which allow one to reduce the one-dimensional Schrödinger equation to a named equation of mathematical physics, namely either Bessel’s or Whittaker’s differential equation. In all cases, we provide closed form expressions for both the symmetric and antisymmetric wavefunction solutions, each along with an associated transcendental equation for allowed eigenvalues. The class of potentials considered contains an example of both cusp-like single wells and a double-well.

scholarly journals Interaction between Different Kinds of Quantum Phase Transitions

2021 ◽  
Vol 3 (2) ◽  
pp. 253-261
Author(s):  
Angel Ricardo Plastino ◽  
Gustavo Luis Ferri ◽  
Angelo Plastino
Keyword(s):  
Phase Transitions ◽  
Nuclear Physics ◽  
Body Problem ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Many Body ◽  
Pairing Interaction ◽  
Exactly Solvable

We employ two different Lipkin-like, exactly solvable models so as to display features of the competition between different fermion–fermion quantum interactions (at finite temperatures). One of our two interactions mimics the pairing interaction responsible for superconductivity. The other interaction is a monopole one that resembles the so-called quadrupole one, much used in nuclear physics as a residual interaction. The pairing versus monopole effects here observed afford for some interesting insights into the intricacies of the quantum many body problem, in particular with regards to so-called quantum phase transitions (strictly, level crossings).

scholarly journals Exactly solvable models in arbitrary dimensions

1998 ◽  
Vol 238 (4-5) ◽  
pp. 213-218 ◽  
Author(s):  
Ranjan Kumar Ghosh ◽  
Sumathi Rao
Keyword(s):  
Exactly Solvable Models ◽  
Solvable Models ◽  
Exactly Solvable ◽  
Arbitrary Dimensions

Exactly solvable models for trapped boson systems

2004 ◽  
Vol 243 (1-6) ◽  
pp. 131-143 ◽  
Author(s):  
J. Dukelsky ◽  
G.G. Dussel ◽  
S. Pittel
Keyword(s):  
Exactly Solvable Models ◽  
Solvable Models ◽  
Boson Systems ◽  
Exactly Solvable

scholarly journals Exactly solvable models through the empty-interval method

2001 ◽  
Vol 64 (5) ◽  
Author(s):  
M. Alimohammadi ◽  
M. Khorrami ◽  
A. Aghamohammadi
Keyword(s):  
Exactly Solvable Models ◽  
Solvable Models ◽  
Empty Interval ◽  
Interval Method ◽  
Exactly Solvable
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