A canonical approach for computing the eigenvalues of the Schrödinger equation for double-well potentials

2000 ◽  
Vol 78 (11) ◽  
pp. 969-976 ◽  
Author(s):  
M Korek ◽  
K Fakhreddine
Keyword(s):  
Integral Equation ◽  
Wave Function ◽  
Schrödinger Equation ◽  
Volterra Integral Equation ◽  
Schrodinger Equation ◽  
High Accuracy ◽  
Present Formulation ◽  
Numerical Application ◽  
Canonical Approach ◽  
Double Well Potential

The problem of obtaining the eigenvalues of the Schrödinger equation for a double-well potential function is considered. By replacing the differential Schrödinger equation by a Volterra integral equation the wave function will be given by [Formula: see text] where the coefficients ai are obtained from the boundary conditions and the fi are two well-defined canonical functions. Using these canonical functions, we define an eigenvalue function F(E) = 0; its roots E1, E2, ... are the eigenvalues of the corresponding double-well potential. The numerical application to analytical potentials (either symmetric or asymmetric) and to a numerical potential of the (2)1 [Formula: see text] state of the molecule Na2 shows the validity and the high accuracy of the present formulation. PACS No.: 03.65Ge

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

COLLECTIVE SPIN BY LINEARIZATION OF THE SCHRÖDINGER EQUATION FOR NUCLEAR COLLECTIVE MOTION

1988 ◽  
Vol 03 (09) ◽  
pp. 859-866 ◽  
Author(s):  
MARTIN GREINER ◽  
WERNER SCHEID ◽  
RICHARD HERRMANN
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Degrees Of Freedom ◽  
Collective Motion ◽  
First Order ◽  
Energy And Momentum

The free Schrödinger equation for multipole degrees of freedom is linearized so that energy and momentum operators appear only in first order. As an example, we demonstrate the linearization procedure for quadrupole degrees of freedom. The wave function solving this equation carries a spin. We derive the operator of the collective spin and its eigenvalues depending on multipolarity.

On the Vanishing of the Cosmological Vacuum Energy

1997 ◽  
Vol 12 (16) ◽  
pp. 1127-1130 ◽  
Author(s):  
M. D. Pollock
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Vacuum Energy ◽  
Ground State Solution ◽  
Space Time ◽  
State Solution ◽  
Superstring Theory ◽  
The Universe

By demanding the existence of a globally invariant ground-state solution of the Wheeler–De Witt equation (Schrödinger equation) for the wave function of the Universe Ψ, obtained from the heterotic superstring theory, in the four-dimensional Friedmann space-time, we prove that the cosmological vacuum energy has to be zero.

scholarly journals Angular distribution of scission neutrons studied with time-dependent Schrödinger equation

2018 ◽  
Vol 169 ◽  
pp. 00029
Author(s):  
Takahiro Wada ◽  
Tomomasa Asano ◽  
Nicolae Carjan
Keyword(s):  
Wave Function ◽  
Angular Distribution ◽  
Schrödinger Equation ◽  
Time Evolution ◽  
Schrodinger Equation ◽  
Initial Distribution ◽  
Time Dependent ◽  
Heavy Fragment ◽  
Fission Fragments ◽  
Asymmetric Fission

We investigate the angular distribution of scission neutrons taking account of the effects of fission fragments. The time evolution of the wave function of the scission neutron is obtained by integrating the time-dependent Schrodinger equation numerically. The effects of the fission fragments are taken into account by means of the optical potentials. The angular distribution is strongly modified by the presence of the fragments. In the case of asymmetric fission, it is found that the heavy fragment has stronger effects. Dependence on the initial distribution and on the properties of fission fragments is discussed. We also discuss on the treatment of the boundary to avoid artificial reflections

ON THE SEMI-CLASSICAL APPROXIMATION TO THE SUPERSTRING THEORY

1992 ◽  
Vol 07 (25) ◽  
pp. 6421-6430 ◽  
Author(s):  
M.D. POLLOCK
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Classical Limit ◽  
Schrodinger Equation ◽  
Cosmic Time ◽  
Canonical Coordinates ◽  
Superstring Theory ◽  
Higher Derivative ◽  
Effective Lagrangian ◽  
Non Locality

The semi-classical limit of the compactified, heterotic superstring theory is examined, including the effects of higher-derivative terms [Formula: see text] in the effective Lagrangian. The total wave-function Ψ obeys a Schrödinger equation in the mini-superspace ds2=dt2−e2α(t)dx2, the canonical coordinates being the position α and the velocity (Hubble parameter) [Formula: see text], while the cosmic time coincides with the parameter introduced by Tomonaga, ∂/∂σ≡∂/∂t≡ξ∂/∂α. The wave function describing the matter, Ψ m , also obeys a linear Schrödinger equation. The relevance of this result to the problem of non-locality in quantum mechanics is discussed.

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