SOLVING THE SCHRÖDINGER EQUATION FOR BOUND STATES WITH MATHEMATICA 3.0

Using Mathematica 3.0, the Schrödinger equation for bound states is solved. The method of solution is based on a numerical integration procedure together with convexity arguments and the nodal theorem for wave functions. The interaction potential has to be spherically symmetric. The solving procedure is simply defined as some Mathematica function. The output is the energy eigenvalue and the reduced wave function, which is provided as an interpolated function (and can thus be used for the calculation of, e.g., moments by using any Mathematica built-in function) as well as plotted automatically. The corresponding program schroedinger.nb can be obtained from [email protected].

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SCHRÖDINGER EQUATION FOR HEAVY MESONS EXPANDED IN 1/mQ

Modern Physics Letters A ◽

10.1142/s0217732396000291 ◽

1996 ◽

Vol 11 (03) ◽

pp. 257-266 ◽

Cited By ~ 4

Author(s):

TAKAYUKI MATSUKI

Keyword(s):

Wave Function ◽

Perturbation Theory ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Bound States ◽

Higher Order ◽

Wave Functions ◽

Heavy Mesons ◽

Higher Order Corrections

Operating just once the naive Foldy-Wouthuysen-Tani transformation on the Schrödinger equation for [Formula: see text] bound states described by a Hamiltonian, we systematically develop a perturbation theory in 1/mQ which enables one to solve the Schrödinger equation to obtain masses and wave functions of the bound states in any order of 1/mQ. There also appear negative components of the wave function in our formulation which contribute also to higher order corrections to masses.

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EXACT SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH SPHERICALLY SYMMETRIC OCTIC POTENTIAL

Modern Physics Letters A ◽

10.1142/s021773231250112x ◽

2012 ◽

Vol 27 (20) ◽

pp. 1250112 ◽

Cited By ~ 12

Author(s):

DAVIDS AGBOOLA ◽

YAO-ZHONG ZHANG

Keyword(s):

Schrödinger Equation ◽

Exact Solutions ◽

Closed Form ◽

Schrodinger Equation ◽

Wave Functions ◽

Spherically Symmetric ◽

Algebraic Equations ◽

Potential Parameters

We present exact solutions of the Schrödinger equation with spherically symmetric octic potential. We give closed-form expressions for the energies and the wave functions as well as the allowed values of the potential parameters in terms of a set of algebraic equations.

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Dirac Bound States of the Killingbeck Potential Under External Magnetic Fields

Zeitschrift für Naturforschung A ◽

10.1515/zna-2015-0021 ◽

2015 ◽

Vol 70 (7) ◽

pp. 499-505 ◽

Cited By ~ 8

Author(s):

Zahra Sharifi ◽

Fateme Tajic ◽

Majid Hamzavi ◽

Sameer M. Ikhdair

Keyword(s):

Wave Function ◽

Magnetic Fields ◽

Ground State ◽

Bound States ◽

State Energy ◽

Potential Model ◽

Energy Levels ◽

Energy Eigenvalue ◽

Wave Functions ◽

Ansatz Method

AbstractThe Killingbeck potential model is used to study the influence of the external magnetic and Aharanov–Bohm (AB) flux fields on the splitting of the Dirac energy levels in a 2+1 dimensions. The ground state energy eigenvalue and its corresponding two spinor components wave functions are investigated in the presence of the spin and pseudo-spin symmetric limit as well as external fields using the wave function ansatz method.

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EXACT SOLUTIONS OF THE MODIFIED KRATZER POTENTIAL PLUS RING-SHAPED POTENTIAL IN THE D-DIMENSIONAL SCHRÖDINGER EQUATION BY THE NIKIFOROV–UVAROV METHOD

International Journal of Modern Physics C ◽

10.1142/s0129183108012030 ◽

2008 ◽

Vol 19 (02) ◽

pp. 221-235 ◽

Cited By ~ 62

Author(s):

SAMEER M. IKHDAIR ◽

RAMAZAN SEVER

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Bound States ◽

Laguerre Polynomials ◽

Three Dimensional ◽

Wave Functions ◽

Modified Kratzer Potential ◽

Energy Bound ◽

Uvarov Method ◽

Exact Energy

We present analytically the exact energy bound-states solutions of the Schrödinger equation in D dimensions for a recently proposed modified Kratzer plus ring-shaped potential by means of the Nikiforov–Uvarov method. We obtain an explicit solution of the wave functions in terms of hyper-geometric functions (Laguerre polynomials). The results obtained in this work are more general and true for any dimension which can be reduced to the well-known three-dimensional forms given by other works.

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Solutions of the D-Dimensional Schrödinger Equation with the Hyperbolic Pöschl-Teller Potential plus Modified Ring-Shaped Term

Advances in High Energy Physics ◽

10.1155/2018/4536543 ◽

2018 ◽

Vol 2018 ◽

pp. 1-9 ◽

Cited By ~ 2

Author(s):

Ibsal A. Assi ◽

Akpan N. Ikot ◽

E. O. Chukwuocha

Keyword(s):

Wave Function ◽

Energy Level ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Wave Functions ◽

Radial Equation ◽

Energy Eigenvalues ◽

Separation Of Variable ◽

Nu Method ◽

Hyperspherical Coordinate

We solve the D-dimensional Schrödinger equation with hyperbolic Pöschl-Teller potential plus a generalized ring-shaped potential. After the separation of variable in the hyperspherical coordinate, we used Nikiforov-Uvarov (NU) method to solve the resulting radial equation and obtain explicitly the energy level and the corresponding wave function in closed form. The solutions to the energy eigenvalues and the corresponding wave functions are obtained using the NU method as well.

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Spectroscopy of Heavy Mesons Expanded in 1/mQ

Australian Journal of Physics ◽

10.1071/p96038 ◽

1997 ◽

Vol 50 (1) ◽

pp. 163 ◽

Cited By ~ 5

Author(s):

Takayuki Matsuki ◽

Toshiyuki Mori

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Bound States ◽

Heavy Meson ◽

Order Equation ◽

Wave Functions ◽

Meson Spectrum ◽

Heavy Quark Mass ◽

Complete Set ◽

Scalar Potentials

Operating just once with the naive Foldy–Wouthuysen–Tani transformation on the Schrödinger equation for Qq bound states, described by the Hamiltonian which includes Coulomb-like as well as confining scalar potentials, we have calculated the heavy meson spectrum of D, D*, B and B*. Based on a formulation recently proposed, their masses and wave functions are expanded in 1=mQ, with a heavy quark mass mQ, up to the second order. The lowest order equation is examined carefully to obtain a complete set of eigenfunctions for the Schrödinger equation.

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ANALYSIS OF ENERGY AND WAVE FUNCTIONS AND THE THERMODYNAMICS PROPERTIES OF THE 6-DIMENSIONAL SCHRODINGER EQUATION UNDER DOUBLE RING-SHAPE OSCILLATOR (DRSO) AND MANNING-ROSEN POTENTIALS USING SUSY QM METHOD

Periódico Tchê Química ◽

10.52571/ptq.v17.n36.2020.580_periodico36_pgs_565_583.pdf ◽

2020 ◽

Vol 17 (36) ◽

pp. 565-583

Author(s):

Dedy Adrianus BILAUT ◽

A SUPARMI ◽

C CARI ◽

Suci FANIANDARI

Keyword(s):

Free Energy ◽

Wave Function ◽

Thermodynamic Properties ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Wave Functions ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Double Ring ◽

Angular Quantum Number

The exact solutions of the Schrodinger equations (SE) in the D-dimensional coordinate system have attracted the attention of many theoretical researchers in branches of quantum physics and quantum chemistry. The energy eigenvalues and the wave function are the solutions of the Schrodinger equation that implicitly represents the behavior of a quantum mechanical system. This study aimed to obtain the eigenvalues, wave functions, and thermodynamic properties of the 6-Dimensional Schrodinger equation under Double Ring-Shaped Oscillator (DRSO) and Manning-Rosen potential. The variable separation method was applied to reduce the one 6-Dimensional Schrodinger equation depending on radial and angular non-central potential into five onedimensional Schrodinger equations: one radial and five angular Schrodinger equations. Each of these onedimensional Schrodinger equations was solved using the SUSY QM method to obtain one eigenvalue and one wave function of the radial part, five eigenvalues, and five angular wave functions angular part. Some thermodynamic properties such, the vibrational mean energy 𝑈, vibrational specific heat 𝐶, vibrational free energy 𝐹, and vibrational entropy 𝑆, were obtained using the radial energy equations. The results showed that except the 𝑛𝑙1, all increment of angular quantum number decreases the energy values. Increments of all potential parameter increase the energy values. Increment of angular quantum number and potentials parameter increases the amplitude and shifts the wave functions to the left. However, the increment of 𝑛𝑙1, 𝛼, 𝜎, and 𝜌 decrease the amplitude and shift wavefunctions to the right. Moreover, the vibrational mean energy 𝑈 and free energy 𝐹 increased as the increasing value of potentials parameters, where the ω parameter has the dominant effect than the other parameters. The vibrational specific heat 𝐶 and entropy 𝑆 affected only by the 𝜔 parameter, where 𝐶 and 𝑆 decreased as the increase of 𝜔.

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The Analytical Solutions of the Schrodinger Equation for a Single Electron in the Nikiforov-Uvarov Framework

Jurnal Fisika ◽

10.15294/jf.v10i2.25190 ◽

2020 ◽

Vol 10 (2) ◽

pp. 1-10

Author(s):

Yacobus Yulianto ◽

Zaki Su'ud

Keyword(s):

Wave Function ◽

Schrödinger Equation ◽

Analytical Solutions ◽

Schrodinger Equation ◽

Quantum Physics ◽

Energy Eigenvalue ◽

Single Electron ◽

Alternative Procedure ◽

Alternative Method ◽

Uvarov Method

In this study, it is intended to show an alternative method to derive the wave function of a single electron as solutions of the Schrodinger equation. The Nikiforov-Uvarov method was chosen to be utilized since this method can solve the Schrodinger equation with several well-known potentials in the non-relativistic mechanics of quantum. The obtained results of this study have succeed to explain the wave function and the energy eigenvalue for a single electron as lectured in quantum physics textbooks. These results prove that the Nikiforov-Uvarov method provides an alternative procedure to solve the Schrodinger equation.

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Wave Function Properties and Shifted Energy Levels of Bound States in a Plasma

Zeitschrift für Naturforschung A ◽

10.1515/zna-1991-0704 ◽

1991 ◽

Vol 46 (7) ◽

pp. 583-589 ◽

Cited By ~ 1

Author(s):

H. Lehmann ◽

W. Ebeling

Keyword(s):

Wave Function ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Bound States ◽

Energy Levels ◽

Plasma Composition ◽

Energy Eigenvalues ◽

Electron Positron ◽

New Energy ◽

Variation Procedure

On the basis of earlier work we show a simple way to estimate the properties of bound states in a plasma. The Bethe-Salpeter equation is approximated by an effective Schrodinger equation. The energy eigenvalues are found via a variation procedure. The treatment is applicated to helium-like bound states and excited hydrogen-like states. The effect of the new energy eigenvalues on the plasma composition is discussed for the symmetrical electron-positron plasma.

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