Solving the Schroedinger equation for bound states with Mathematica 3.0

Abstract

Using Mathematica 3.0, the Schroedinger 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.

LaTeX, 11 pages, 2 figures; minor change in program listing

Cited by in corpus (95)

• Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
• A non-relativistic model for the $[cc][\bar{c}\bar{c}]$ tetraquark
• Quarkonium Hybrids with Nonrelativistic Effective Field Theories
• Heavy Quarkonium Spectrum at $\mathcal{O}({\alpha }_s^5{m}_q)$ and Bottom/Top Quark Mass Determination
• Mass spectra and Regge trajectories of ${\Lambda }_c^{+}$, ${\Sigma }_c^0$, ${\Xi }_c^0$ and ${\Omega }_c^0$ Baryons
• Excited State Mass spectra of doubly heavy baryons ${\Omega }_{cc}$, ${\Omega }_{bb}$ and ${\Omega }_{bc}$
• $Q\bar{Q}$ ($Q\in \{b,c\}$) spectroscopy using Cornell potential
• Photoproduction of Charmonia and Total Charmonium-Proton Cross Sections
• The approach to equilibrium of a quarkonium in a quark-gluon plasma
• The newly observed open-charm states in quark model
• Excited bottom and bottom-strange mesons in the quark model
• An approximate κ state solutions of the Dirac equation for the generalized Morse potential under spin and pseudospin symmetry
• Excited State Mass spectra and Regge trajectories of Bottom Baryons
• Excited State Mass spectra of Singly Charmed Baryons
• Excited state mass spectra of doubly heavy $\Xi$ baryons
• On the bound-state solutions of the Manning-Rosen potential including improved approximation to the orbital centrifugal term
• Canonical Charmonium Interpretation for Y(4360) and Y(4660)
• Thermal Properties of Deng-Fan-Eckart Potential model using Poisson Summation Approach
• Bound state solutions of the Manning-Rosen potential
• Properties of $Q\bar{Q}$ $(Q\epsilon b,c)$ mesons in Coulomb plus Power potential
• Resonant Dark Matter
• Improved analytical approximation to arbitrary l-state solutions of the Schrodinger equation for the hyperbolical potentials
• Mass spectra of four quark states in hidden charm sector
• Nonrelativistic model of tetraquarks and predictions for their masses from fits to charmed and bottom meson data
• Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein-Gordon equation for the scalar and vector Hulthen potentials
• Theoretical uncertainties in exclusive electroproduction S-wave heavy quarkonia
• Relativistic Harmonic Oscillator
• Implication of BaBar's new data on the $D_{s1}(2710)$ and $D_{sJ}(2860)$
• Extraction of ground-state decay constant from dispersive sum rules: QCD vs potential models
• $O({\alpha }_s{v}^2)$ Corrections to Hadronic and Electromagnetic Decays of ${}^1{S}_0$ Heavy Quarkonium
• Modes with variable mass as an alternative in AdS / QCD models with chiral symmetry breaking
• Spectrum of strange singly charmed baryons in the constituent quark model
• Decay rates of charmonia within a quark-antiquark confining potentials
• Mass Spectra and Decay Properties of Singly Heavy Bottom-Strange Baryons
• Spectrum of nonstrange singly charmed baryons in the constituent quark model
• Spectroscopy of light $N^{\ast }$ baryons
• Spectroscopy of ${\Omega }_{ccb}$ baryon in Hypercentral Quark Model
• Spectroscopy of all charm tetraquark states
• Spectroscopic Investigation of Light Strange S=-1 $\Lambda$, $\Sigma$ and S=-2 $\Xi$ Baryons
• Spectroscopy of Light Baryons: $\Delta$ Resonances
• Quality of Variational Trial States
• Spectroscopic Study of Strangeness=-3 ${\Omega }^{-}$ Baryon
• Relativistic corrections to double charmonium production in high energy proton-proton interaction
• Two-Photon, Two-gluon and Radiative Decays of Heavy Flavoured Mesons
• Phenomenological study of quarkonium suppression and the impact of the energy gap between singlets and octets
• The charmed strange meson system
• Studies on bound-state spectra of Manning-Rosen potential
• Approximated l-states of the Manning-Rosen potential by Nikiforov-Uvarov method
• $Z_b(10650)$ and $Z_b(10610)$ states in a chiral quark model
• Spectroscopic properties of $\Delta$ Baryons
• Y(4260) --> gamma + X(3872) in the diquarkonium picture
• The problem of uniqueness in the reduced description of adsorption on the wedge-shaped substrate
• Relativistic corrections to the pair double heavy diquark production in e^+e^- annihilation
• Spectra and decay properties of ${\Lambda }_b$ and ${\Sigma }_b$ baryons
• Relativistic description of asymmetric fully heavy tetraquarks in the diquark-antidiquark model
• It is a Graviton! or maybe not
• Arbitrary $\ell$-state solutions of the Klein-Gordon equation with the Eckart plus a class of Yukawa potential and its non-relativistic thermal properties
• The Spinless Relativistic Woods-Saxon Problem
• Relativistic corrections to the pair $B_c$-meson production in $e^{+}{e}^{-}$ annihilation
• Psi' to J/Psi Ratio in Diffractive Photoproduction
• Analytical solution of $D$ dimensional Schrödinger equation for Eckart potential with a new improved approximation in centrifugal term
• Higgs boson decay to paired $B_c$: relativistic and one-loop corrections
• Chi_b(3P) splitting predictions in potential models
• Mass-Spectroscopy of hidden charm and hidden strange tetraquarks in diquark-antidiquark approach
• The complex heavy-quark potential in an anisotropic quark-gluon plasma -- Statics and dynamics
• Relativistic corrections to paired production of charmonium and bottomonium in decays of the Higgs boson
• Ro-vibrational energy analysis of Manning-Rosen and Pöschl-Teller potentials with a new improved approximation in the centrifugal term
• The auxiliary field method in quantum mechanics
• Eigenstates with the auxiliary field method
• Tetraquark states in the bottom sector and the status of the $Y_b$(10890) state
• Charmonium Properties Using the Discrete Variable Representation (DVR) Method
• A chiral symmetry breaking AdS / QCD model with scalar interactions
• Bottomonium spectroscopy motivated by general features of pNRQCD
• Exclusive double $B_c$ meson production from $e^{+}{e}^{-}$ annihilation into two virtual photons
• Higgs boson decay to the pair of S- and P-wave $B_c$ mesons
• Spectroscopic Study of ${\Omega }_{cc}$, ${\Omega }_{cb}$ and ${\Omega }_{bb}$ Baryons
• Possible $D\bar{D}$ and $B\bar{B}$ Molecular states in a chiral quark model
• The Spinless Relativistic Hulthén Problem
• Models and Potentials in Hadron Spectroscopy
• Studies on the bound-state spectrum of hyperbolic potential
• The Spinless Relativistic Yukawa Problem
• Masses of Heavy-Light mesons with two loop static potential in a Variational approach
• Relativistic corrections to η_c-pair production in high energy proton-proton collisions
• Electric Polarizability of Mesons in Semirelativistic Quark Models
• Complete analytical solution to the Cornell potential and heavy quarkonium structure
• Spectroscopy of heavy-heavy flavour mesons and annihilation widths of quarkonia
• New near-threshold mesons
• Theoretical determination of etab's electromagnetic decay width
• Decay Properties of $D$ and $D_s$ mesons
• Semileptonic decay and form factors of ${\Omega }_b^{-}\to {\Omega }_c^{0}e\overline{{\nu }_e}$
• Numerical Solution of the Spinless Salpeter Equation by a Semianalytical Matrix Method (a Mathematica 4.0 routine)
• Mass spectroscopy of charmonium using a screened potential
• Beauty Hadron Spectrum in a Screened Potential Model
• Bound-state properties from field-theory correlators
• Mass-Spectroscopy of [$bb][\bar{b}\bar{b}$] and [$bq][\bar{b}\bar{q}$] tetraquark states in a diquark-antidiquark formalism