Estimating ground-state energies in supersymmetric quantum mechanics: (2) Unbroken case

1983 ◽  
Vol 20 (3) ◽  
pp. 227-236 ◽  
Author(s):  
R. B. Abbott ◽  
W. J. Zakrzewski
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Supersymmetric Quantum Mechanics ◽  
Ground State Energies

Calculation of energy eigenvalues via supersymmetric quantum mechanics

1989 ◽  
Vol 67 (10) ◽  
pp. 931-934 ◽  
Author(s):  
Francisco M. Fernández ◽  
Q. Ma ◽  
D. J. DeSmet ◽  
R. H. Tipping
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Potential Energy Function ◽  
Supersymmetric Quantum Mechanics ◽  
Energy Eigenvalues ◽  
Arbitrary Power ◽  
Rational Function Approximation ◽  
Ricatti Equation ◽  
Original Potential ◽  
Ground State Energies

A systematic procedure using supersymmetric quantum mechanics is presented for calculating the energy eigenvalues of the Schrödinger equation. Starting from the Hamiltonian for a given potential-energy function, a sequence of supersymmetric partners is derived such that the ground-state energy of the kth one corresponds to the kth eigen energy of the original potential. Various theoretical procedures for obtaining ground-state energies, including a method involving a rational-function approximation for the solution of the Ricatti equation that is outlined in the present paper, can then be applied. Illustrative numerical results for two one-dimensional parity-invariant model potentials are given, and the results of the present procedure are compared with those obtainable via other methods. Generalizations of the method for arbitrary power-law potentials and for radial problems are discussed briefly.

Quantum Mechanics

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Variational Principles ◽  
Free Particle ◽  
Uncertainty Relations ◽  
Probabilistic Interpretation ◽  
Historical Account ◽  
Potential Wells ◽  
Harmonic Oscillator Potential ◽  
Ground State Energies

In this chapter, the main features of quantum theory are presented. The chapter begins with a historical account of the invention of quantum mechanics. The meaning of position and momentum in quantum mechanics is discussed and non-commuting operators are introduced. The Schrödinger equation is presented and solved for a free particle and for a harmonic oscillator potential in one dimension. The meaning of the wavefunction is considered and the probabilistic interpretation is presented. The mathematical machinery and language of quantum mechanics are developed, including Hermitian operators, observables and expectation values. The uncertainty principle is discussed and the uncertainty relations are presented. Scattering and tunnelling by potential wells and barriers is considered. The use of variational principles to estimate ground state energies is explained and illustrated with a simple example.

ORTHOSUPERSYMMETRIC QUANTUM MECHANICS

1993 ◽  
Vol 08 (07) ◽  
pp. 1245-1257 ◽  
Author(s):  
AVINASH KHARE ◽  
A.K. MISHRA ◽  
G. RAJASEKARAN
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Supersymmetric Quantum Mechanics ◽  
Closed Algebra ◽  
New Form ◽  
Dilatation Generator ◽  
Conformal Generator

We construct a new form of supersymmetric quantum mechanics named orthosupersymmetric quantum mechanics. We show that there are p orthosupercharges Qα (α= 1,2, …, p) which satisfy the algebra [Formula: see text] where H is the Hamiltonian. The spectra of this class of systems are shown to be (p+1)-fold degenerate, at least above the ground state. We also discuss a model of conformal orthosupersymmetry of degree p and show that in this case there are p orthosupercharges, and p conformal orthosupercharges which along with H, dilatation generator D and conformal generator K form a closed algebra. A comparative discussion on parasupersymmetric and orthosupersymmetric quantum mechanics is also given.

Exact solutions for the potential V(r) = r2 + β/r4 + λ/r6 by supersymmetric quantum mechanics

1995 ◽  
Vol 73 (7-8) ◽  
pp. 519-525 ◽  
Author(s):  
Y. P. Varshni ◽  
Nivedita Nag ◽  
Rajkumar Roychoudhury
Keyword(s):  
Quantum Mechanics ◽  
Exact Solutions ◽  
Excited States ◽  
Ground State ◽  
Supersymmetric Quantum Mechanics

A method based on supersymmetric quantum mechanics is given for obtaining exact solutions of the potential V(r) = r2 + β/r4 + λ/r6, where β and λ are parameters, provided a certain constraint is satisfied between β and λ. Detailed results are given for the ground state as well as for several excited states. A method for determining the exact energies of two levels for the same values of β and λ is given and illustrated by examples.

Ground state structure in supersymmetric quantum mechanics

1987 ◽  
Vol 178 (2) ◽  
pp. 313-329 ◽  
Author(s):  
Arthur Jaffe ◽  
Andrzej Lesniewski ◽  
Maciej Lewenstein
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Supersymmetric Quantum Mechanics ◽  
Ground State Structure ◽  
State Structure
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