scholarly journals Evolution and Dynamics of Quantum Fluids

2021 ◽  
Author(s):  
Sohan Sengupta
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dynamical Equation ◽  
Stellar Dynamics ◽  
Quantum Fluids ◽  
Full Description ◽  
Semiclassical Approach ◽  
Quantum Fluid ◽  
Quantum Dynamical ◽  
New Equation

Abstract Quantum Fluids follow Quantum Dynamical Equation(s), which were not known till date. There exist a set of two equations, that is semiclassical approach to Quantum Fluids called Madelung’s Equations. But a new fully quantum variant of Madelung’s Equations when embedded in the Schrodinger Equation is gives full description of evolution of Quantum fluid with respect to time and position. The equation presented in this article has two unknown variables, one is density and other is velocity field as a function of spatial and time coordinates. The equation presented in this article, is derived from Schrodinger Equation, obeying Continuity equation, and Navier Strokes Equation. Bohm’s potential were externally added in Madeline’s equation. But the new equation which is fully quantum mechanical in nature; Bohm’s potential appears out of the equation, which is interesting to observe. Astrophysical cold stellar dynamics and condensed fluids have the main application of this equation. Quantum fluids show strange behaviour when compared to normal fluids. It is also shown that quantum fluid also have spins which has no classical analog.

Quantum Dynamics Using The Time-Dependent Schrödinger Equation

2006 ◽  
Author(s):  
Abraham Nitzan
Keyword(s):  
Schrödinger Equation ◽  
Quantum Dynamics ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Full Description ◽  
Quantum Mechanical ◽  
Condensed Phases ◽  
Full Picture ◽  
Linear Differential ◽  
External Forces

This chapter focuses on the time-dependent Schrödinger equation and its solutions for several prototype systems. It provides the basis for discussing and understanding quantum dynamics in condensed phases, however, a full picture can be obtained only by including also dynamical processes that destroy the quantum mechanical phase. Such a full description of quantum dynamics cannot be handled by the Schrödinger equation alone; a more general approach based on the quantum Liouville equation is needed. This important part of the theory of quantum dynamics is discussed in Chapter 10. Given a system characterized by a Hamiltonian Ĥ , the time-dependent Schrödinger equation is For a closed, isolated system Ĥ is time independent; time dependence in the Hamiltonian enters via effect of time-dependent external forces. Here we focus on the earlier case. Equation (1) is a first-order linear differential equation that can be solved as an initial value problem.

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.

Quantum Boxes, Stringed Instruments

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Energy Level ◽  
Schrödinger Equation ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Probability Distributions ◽  
Wave Functions ◽  
Energy Level Diagram ◽  
One Dimensional ◽  
Stringed Instruments ◽  
Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

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