scholarly journals Operator of Time and Generalized Schrödinger Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-4 ◽  
Author(s):  
Slobodan Prvanović
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Discrete Time ◽  
Schrodinger Equation ◽  
Adjoint Operator ◽  
The Self ◽  
The Other ◽  
Nonrelativistic Quantum ◽  
Generalized Schrödinger Equation ◽  
Nonrelativistic Quantum Mechanics

The equation describing the change of the state of the quantum system with respect to energy is introduced within the framework of the self-adjoint operator of time in nonrelativistic quantum mechanics. In this proposal, the operator of time appears to be the generator of the change of the energy, while the operator of energy that is conjugate to the operator of time generates the time evolution. Two examples, one with discrete time and the other with continuous one, are given and the generalization of Schrödinger equation is proposed.

scholarly journals Breve argumentación didáctica de la mecánica cuántica de muchos cuerpos

Respuestas ◽  
2017 ◽  
Vol 22 (1) ◽  
pp. 29
Author(s):  
Cristian Andrés Aguirre-Téllez ◽  
José Barba-Ortega
Keyword(s):  
Quantum Mechanics ◽  
Analytical Solution ◽  
Schrödinger Equation ◽  
Analytical Method ◽  
Schrodinger Equation ◽  
Quantum Systems ◽  
The Self ◽  
Self Consistent ◽  
El Sistema ◽  
Self Consistent Field

El problema general en mecánica cuántica está basado en la solución de una ecuación en valores propios de un operador dado (en una representación adecuada), generalmente  dicho operador es el Hamiltoniano que da cuenta de la interacción energética (salvo que dependa del tiempo) del sistema en cuestión. La solución de la ecuación de Schrödinger permite escribir el comportamiento dinámico del sistema sometido a ciertas restricciones. Sin embargo, la solución analítica de esta ecuación es viable solo en sistemas simples, cuando el sistema se describe desde la interacción de muchas partículas (problema electrónico-base de la construcción de sistemas cuánticos complejos aplicable a la descripción de moléculas, sólidos y sistemas cuánticos interactuantes en general.) la solución de la ecuación de Schrödinger del sistema no se puede realizar vía método analítico; con lo cual existe una forma más global de enfrentar dicho problema, el método auto consistente; mediante el cual se puede solucionar sistemas complejos de muchos cuerpos. Es así que en el presente paper presentamos una comparación entre el sistema auto consistente y algunas variantes que existen, con el método analítico en sistemas demuchos cuerpos y como opera dicho método, esto aplicado a un problema de dos cuerpos con interacción Coulombiana, ya que este problema presenta solución analítica y ha sido extensamente estudiado; esto con la finalidad de que los estudiantes interesados en la materia comprendan como se abordan problemas vía métodos auto consistentes y como opera este método, ya que en la literatura pocas veces se presenta el algoritmo de solución mediante este método.Palabras clave: Mecánica Cuántica, Método Auto-Consistente, problema de dos cuerpos.AbstractThe general problem in quantum mechanics is based on the solution of an equation in eigenvalues of a given operator (in a suitable representation), generally said operator is the Hamiltonian that accounts for the energy interaction (unless it depends on the time) of the system in question. The solution of the Schrodinger equation allows writing the dynamic behavior of the system subject to certain restrictions. however, the analytical solution of this equation is feasible only in simple systems, when the system is described from the interaction of many particles (electronic problem- basis of the construction of complex quantum systems applicable to the description of molecules, solids and interacting quantum systems in general.), the solution of the Schrödinger equation of the system can´t be performed via analytical method; with which there is a more global way of facing this problem, the self-consistent method; through which complex systems of many bodies can be solved. thus, in the present paper we present a comparison between the self-consistent system and some variants that exist, with the analytical method in systems of many bodies and how this method operates, this applied to a problem of two bodies with Coulombian interaction, since this problem presents an analytical solution and has been extensively studied; this in order that students interested in the subject understand how problems are addressed through self-consistent methods and how this method operates, since in the literature rarely the solution algorithm is presented by this method.Keywords: Quantum mechanics, Self Consistent Field, Two body 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

A Student's Guide to the Schrödinger Equation

2020 ◽  
Author(s):  
Daniel A. Fleisch
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Plain Language ◽  
Science And Engineering ◽  
Popular Approach ◽  
Matlab Code ◽  
Mathematical Techniques

Quantum mechanics is a hugely important topic in science and engineering, but many students struggle to understand the abstract mathematical techniques used to solve the Schrödinger equation and to analyze the resulting wave functions. Retaining the popular approach used in Fleisch's other Student's Guides, this friendly resource uses plain language to provide detailed explanations of the fundamental concepts and mathematical techniques underlying the Schrödinger equation in quantum mechanics. It addresses in a clear and intuitive way the problems students find most troublesome. Each chapter includes several homework problems with fully worked solutions. A companion website hosts additional resources, including a helpful glossary, Matlab code for creating key simulations, revision quizzes and a series of videos in which the author explains the most important concepts from each section of the book.

scholarly journals Coordinate representation for non-Hermitian position and momentum operators

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170434 ◽  
Author(s):  
F. Bagarello ◽  
F. Gargano ◽  
S. Spagnolo ◽  
S. Triolo
Keyword(s):  
Quantum Mechanics ◽  
The Self ◽  
The Other ◽  
Alternative Strategy ◽  
Coordinate Representation ◽  
Suitable Sense ◽  
Adjoint Operators ◽  
Ordinary Quantum

In this paper, we undertake an analysis of the eigenstates of two non-self-adjoint operators q ^ and p ^ similar, in a suitable sense, to the self-adjoint position and momentum operators q ^ 0 and p ^ 0 usually adopted in ordinary quantum mechanics. In particular, we discuss conditions for these eigenstates to be biorthogonal distributions , and we discuss a few of their properties. We illustrate our results with two examples, one in which the similarity map between the self-adjoint and the non-self-adjoint is bounded, with bounded inverse, and the other in which this is not true. We also briefly propose an alternative strategy to deal with q ^ and p ^ , based on the so-called quasi *-algebras .

Sign in / Sign up

Export Citation Format

Share Document