Solving the one‐dimensional quantum mechanics problems using the matter wave multireflection

1993 ◽  
Vol 74 (2) ◽  
pp. 777-782 ◽  
Author(s):  
Wiesl/aw Polak
Keyword(s):  
Quantum Mechanics ◽  
Matter Wave ◽  
One Dimensional ◽  
The One

Quantum mechanics on (anti)-de Sitter background II: Ramsauer–Townsend effect and WKB method

2018 ◽  
Vol 33 (26) ◽  
pp. 1850150 ◽  
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Energy Level ◽  
Harmonic Oscillator ◽  
Wkb Method ◽  
De Sitter ◽  
Quantum Harmonic Oscillator ◽  
One Dimensional ◽  
Sitter Background ◽  
The One

Based on the one-dimensional quantum mechanics on (anti)-de Sitter background [W. S. Chung and H. Hassanabadi, Mod. Phys. Lett. A 32, 26 (2107)], we discuss the Ramsauer–Townsend effect. We also formulate the WKB method for the quantum mechanics on (anti)-de Sitter background to discuss the energy level of the quantum harmonic oscillator and quantum bouncer.

scholarly journals Schrodinger Wave Equation

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Aaron C.H. Davey
Keyword(s):  
Quantum Mechanics ◽  
Wave Equation ◽  
Quantum Theory ◽  
System Change ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
One Dimensional ◽  
Erwin Schrödinger ◽  
The One ◽  
Over Time

The father of quantum mechanics, Erwin Schrodinger, was one of the most important figures in the development of quantum theory. He is perhaps best known for his contribution of the wave equation, which would later result in his winning of the Nobel Prize for Physics in 1933. The Schrodinger wave equation describes the quantum mechanical behaviour of particles and explores how the Schrodinger wave functions of a system change over time. This project is concerned about exploring the one-dimensional case of the Schrodinger wave equation in a harmonic oscillator system. We will give the solutions, called eigenfunctions, of the equation that satisfy certain conditions. Furthermore, we will show that this happens only for particular values called eigenvalues.

scholarly journals TIME-DEPENDENT PARASUPERSYMMETRY IN QUANTUM MECHANICS

1996 ◽  
Vol 11 (26) ◽  
pp. 2095-2104 ◽  
Author(s):  
BORIS F. SAMSONOV
Keyword(s):  
Quantum Mechanics ◽  
Discrete Spectrum ◽  
Schrodinger Equation ◽  
Free Particle ◽  
Time Dependent ◽  
Darboux Transformations ◽  
Integral Of Motion ◽  
One Dimensional ◽  
A Chain ◽  
The One

Parasupersymmetry of the one-dimensional time-dependent Schrödinger equation is established. It is intimately connected with a chain of the time-dependent Darboux transformations. As an example a parasupersymmetric model of nonrelativistic free particle with threefold degenerate discrete spectrum of an integral of motion is constructed.

scholarly journals Superfluids in polymer quantum mechanics

2021 ◽  
pp. 2150045
Author(s):  
Jasel Berra-Montiel ◽  
Elías Castellanos ◽  
Alberto Molgado ◽  
Jonathan Trinidad-García
Keyword(s):  
Quantum Mechanics ◽  
Regular Representation ◽  
Finite Size ◽  
Bose Gas ◽  
Einstein Condensation ◽  
Minimum Length ◽  
Quantization Scheme ◽  
One Dimensional ◽  
Pathological Behavior ◽  
The One

In this work, we analyze the corrections obtained on a homogeneous one-dimensional Bose gas within the high densities limit by means of the non-regular representation of quantum mechanics introduced by the polymer quantization scheme. Thus, starting from the Bogoliubov formalism, we analyze the ground expectation value of the polymer momentum operator in terms of semiclassical states in order to obtain an analytic expression for the ground state energy of the N-body system, which allows us to solve the pathological behavior commonly associated with the one-dimensional Bose–Einstein condensation through the introduction of finite size effects characterized by the contribution of the polymer corrections. We also discuss the speed of sound in our polymer version of the Bose gas and the corresponding relative shift induced by the introduction of a minimum length parameter. Finally, we investigate the emergent superfluid behavior in our polymer model by implementing an appropriate Landau’s criterion. In this case, we are able to consequently analyze the changes in the critical velocity which defines the limit between the superfluid-condensate regions, thus deducing that the polymer length acts as a kind of pseudo-potential which induces a dissipationless flow associated with the superfluid phase even in the absence of self-interactions.

One-dimensional quantum mechanics with Dunkl derivative

2019 ◽  
Vol 34 (24) ◽  
pp. 1950190
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Scalar Product ◽  
Momentum Operator ◽  
Inner Product ◽  
One Dimensional ◽  
Coordinate Representation ◽  
The One ◽  
Infinite Wall

In this paper, we consider the quantum mechanics with Dunkl derivative. We use the Dunkl derivative to obtain the coordinate representation of the momentum operator and Hamiltonian. We introduce the scalar product to find that the momentum is Hermitian under this inner product. We study the one-dimensional box problem (the spin-less particle with mass m confined to the one-dimensional infinite wall). Finally, we discuss the harmonic oscillator problem.

scholarly journals New AdS2 backgrounds and $$ \mathcal{N} $$ = 4 conformal quantum mechanics

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Yolanda Lozano ◽  
Carlos Nunez ◽  
Anayeli Ramirez ◽  
Stefano Speziali
Keyword(s):  
Quantum Mechanics ◽  
Central Charge ◽  
Infinite Family ◽  
Dimensional System ◽  
One Dimensional ◽  
The Family ◽  
The One ◽  
Conformal Quantum Mechanics ◽  
Chern Simons

Abstract We present a new infinite family of Type IIB backgrounds with an AdS2 factor, preserving $$ \mathcal{N} $$ N = 4 SUSY. For each member of the family we propose a precise dual Super Conformal Quantum Mechanics (SCQM). We provide holographic expressions for the number of vacua (the “central charge”), Chern-Simons terms and other non-perturbative aspects of the SCQM. We relate the “central charge” of the one-dimensional system with a combination of electric and magnetic fluxes in Type IIB. The Ramond-Ramond fluxes are used to propose an extremisation principle for the central charge. Other physical and geometrical aspects of these conformal quantum mechanics are analysed.

scholarly journals The Generalized OTOC from Supersymmetric Quantum Mechanics—Study of Random Fluctuations from Eigenstate Representation of Correlation Functions

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 44
Author(s):  
Kaushik Y. Bhagat ◽  
Baibhab Bose ◽  
Sayantan Choudhury ◽  
Satyaki Chowdhury ◽  
Rathindra N. Das ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Quantum Statistical Mechanics ◽  
Supersymmetric Quantum Mechanics ◽  
The Other ◽  
Potential Well ◽  
One Dimensional ◽  
Quantum Randomness ◽  
The One ◽  
The Impact

The concept of the out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. Further, we demonstrate an equivalent formalism of computation using a general time-independent Hamiltonian having well-defined eigenstate representation for integrable Supersymmetric quantum systems. We found that one needs to consider two new correlators apart from the usual one to have a complete quantum description. To visualize the impact of the given formalism, we consider the two well-known models, viz. Harmonic Oscillator and one-dimensional potential well within the framework of Supersymmetry. For the Harmonic Oscillator case, we obtain similar periodic time dependence but dissimilar parameter dependences compared to the results obtained from both micro-canonical and canonical ensembles in quantum mechanics without Supersymmetry. On the other hand, for the One-Dimensional Potential Well problem, we found significantly different time scales and the other parameter dependence compared to the results obtained from non-Supersymmetric quantum mechanics. Finally, to establish the consistency of the prescribed formalism in the classical limit, we demonstrate the phase space averaged version of the classical version of OTOCs from a model-independent Hamiltonian, along with the previously mentioned well-cited models.

scholarly journals Addendum: Considerations about the incompleteness of the Ehrenfest's theorem in quantum mechanics (2021 Eur. J. Phys. 42 065405)

2021 ◽  
Author(s):  
Domenico Giordano ◽  
Pierluigi Amodio
Keyword(s):  
Quantum Mechanics ◽  
Analytical Solution ◽  
Eigenvalue Problem ◽  
Electric Field ◽  
Electric Charge ◽  
One Dimensional ◽  
The One ◽  
External Forces ◽  
Analytical Expressions

Abstract We describe the analytical solution of the eigenvalue problem introduced in our article mentioned in the title and relative to a punctiform electric charge confined in an one-dimensional box in the presence of an electric field. We also derive and discuss the analytical expressions of the external forces acting on the punctiform charge and associated with the boundaries of the one-dimensional box in the presence of the electric field.

scholarly journals Shannon entropy and Fisher information of the one-dimensional Klein–Gordon oscillator with energy-dependent potential

2018 ◽  
Vol 33 (06) ◽  
pp. 1850033 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Malika Labidi
Keyword(s):  
Quantum Mechanics ◽  
Fisher Information ◽  
Shannon Entropy ◽  
One Dimensional ◽  
Probability Densities ◽  
Klein Gordon ◽  
Dependent Potential ◽  
The One ◽  
Energy Dependent ◽  
Ordinary Quantum

In this paper, we studied, at first, the influence of the energy-dependent potentials on the one-dimensionless Klein–Gordon oscillator. Then, the Shannon entropy and Fisher information of this system are investigated. The position and momentum information entropies for the low-lying states n = 0, 1, 2 are calculated. Some interesting features of both Fisher and Shannon densities, as well as the probability densities, are demonstrated. Finally, the Stam, Cramer–Rao and Bialynicki–Birula–Mycielski (BBM) inequalities have been checked, and their comparison with the regarding results have been reported. We showed that the BBM inequality is still valid in the form [Formula: see text], as well as in ordinary quantum mechanics.

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