scholarly journals A SCHRÖDINGER EQUATION FOR MINIUNIVERSES

1995 ◽  
Vol 10 (05) ◽  
pp. 611-633 ◽  
Author(s):  
MARCO CAVAGLIÀ ◽  
VITTORIO DE ALFARQ ◽  
ALEXANDRE T. FILIPPOV
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Finite Number ◽  
Schrodinger Equation ◽  
Degrees Of Freedom ◽  
Effective Hamiltonian ◽  
Zero Modes ◽  
Walker Metric ◽  
Time Reparametrization Invariance ◽  
Reparametrization Invariance

We discuss how to fix the gauge in the canonical treatment of Lagrangians, with a finite number of degrees of freedom, endowed with time reparametrization invariance. The motion can be described by an effective Hamiltonian acting on the gauge shell canonical space. The system is then suited for quantization. We apply this treatment to the case of a Robertson–Walker metric interacting with zero modes of bosonic fields and write a Schrödinger equation for the on-shell wave function.

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.

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

Introduction

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Degrees Of Freedom ◽  
State Level ◽  
Boltzmann Distribution ◽  
Theoretical Description ◽  
Time Dependent ◽  
Nuclear Dynamics ◽  
Molecular Reaction ◽  
Oppenheimer Approximation

This introductory chapter considers first the relation between molecular reaction dynamics and the major branches of physical chemistry. The concept of elementary chemical reactions at the quantized state-to-state level is discussed. The theoretical description of these reactions based on the time-dependent Schrödinger equation and the Born–Oppenheimer approximation is introduced and the resulting time-dependent Schrödinger equation describing the nuclear dynamics is discussed. The chapter concludes with a brief discussion of matter at thermal equilibrium, focusing at the Boltzmann distribution. Thus, the Boltzmann distribution for vibrational, rotational, and translational degrees of freedom is discussed and illustrated.

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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