Nonrecurrent quantum states: Systems with singular-continuous and discrete spectra

1993 ◽  
Vol 70 (11) ◽  
pp. 1611-1614 ◽  
Author(s):  
Avijit Lahiri
Keyword(s):  
Quantum States ◽  
Continuous And Discrete Spectra ◽  
Discrete Spectra

scholarly journals Special Orthogonal Polynomials in Quantum Mechanics

2019 ◽  
Author(s):  
Abdulaziz D. Alhaidari
Keyword(s):  
Differential Equation ◽  
Quantum Mechanics ◽  
Orthogonal Polynomials ◽  
Solution Space ◽  
Type Equation ◽  
Algebraic Method ◽  
Recursion Relations ◽  
New Class ◽  
Continuous And Discrete Spectra ◽  
Discrete Spectra

Using an algebraic method for solving the wave equation in quantum mechanics, we encountered a new class of orthogonal polynomials on the real line. One of these is a four-parameter polynomial with a discrete spectrum. Another that appeared while solving a Heun-type equation has a mix of continuous and discrete spectra. Based on these results and on our recent study of the solution space of an ordinary differential equation of the second kind with four singular points, we introduce a modification of the hypergeometric polynomials in the Askey scheme. Up to now, all of these polynomials are defined only by their three-term recursion relations and initial values. However, their other properties like the weight function, generating function, orthogonality, Rodrigues-type formula, etc. are yet to be derived analytically. This is an open problem in orthogonal polynomials.

Continuous and Discrete Spectra

2021 ◽  
pp. 75-105
Author(s):  
Victor Lazzarini
Keyword(s):  
Fourier Transform ◽  
Continuous Time ◽  
Audio Signals ◽  
Discrete Form ◽  
Continuous And Discrete Spectra ◽  
Continuous Frequency ◽  
The Fourier Transform ◽  
Discrete Spectra

This chapter explores the spectra of audio signals first from a continuous time and continuous frequency perspective. It starts by reviewing Fourier's theorem and then moves on to put it into its most general form, the Fourier transform. The spectra of simple signals are explored and determined. The operation of convolution is introduced, and through its discrete form, it is applied to the concepts of spectrum and waveform as mediated by the Fourier transform. The chapter is completed with a study of the discrete spectra of classic synthesis waveforms. A revised notion of spectrum is presented at the conclusion.

scholarly journals Nonperturbative Quantization Approach for QED on the Hopf Bundle

Universe ◽  
2021 ◽  
Vol 7 (3) ◽  
pp. 65
Author(s):  
Vladimir Dzhunushaliev ◽  
Vladimir Folomeev
Keyword(s):  
Dirac Equation ◽  
Three Dimensional ◽  
Quantum States ◽  
Classical Solutions ◽  
Dimensional Sphere ◽  
Operator Equations ◽  
Maxwell Fields ◽  
Discrete Spectra ◽  
Infinite Set ◽  
Nonperturbative Quantization

We consider the Dirac equation and Maxwell’s electrodynamics in R×S3 spacetime, where a three-dimensional sphere is the Hopf bundle S3→S2. In both cases, discrete spectra of classical solutions are obtained. Based on the solutions obtained, the quantization of free, noninteracting Dirac and Maxwell fields is carried out. The method of nonperturbative quantization of interacting Dirac and Maxwell fields is suggested. The corresponding operator equations and the infinite set of the Schwinger–Dyson equations for Green’s functions is written down. We write a simplified set of equations describing some physical situations to illustrate the suggested scheme of nonperturbative quantization. Additionally, we discuss the properties of quantum states and operators of interacting fields.

General stability analysis of force-free magnetic fields. Part 2. Application to continuous and discrete spectra of α

1976 ◽  
Vol 15 (1) ◽  
pp. 31-39 ◽  
Author(s):  
Jan Krüger
Keyword(s):  
Stability Analysis ◽  
Magnetic Fields ◽  
General Stability ◽  
Continuous And Discrete Spectra ◽  
Free Fields ◽  
Discrete Spectra

Theorems and criteria on stability of force-free fields, developed in part 1 (Krüger 1976) are illustrated for continuous, as well as discontinuous, spectra of α. Previous and new results are understood from a unified viewpoint.

scholarly journals SUPERSYMMETRIC YANG-MILLS QUANTUM MECHANICS IN VARIOUS DIMENSIONS

2005 ◽  
Vol 20 (19) ◽  
pp. 4484-4491 ◽  
Author(s):  
JACEK WOSIEK
Keyword(s):  
Quantum Mechanics ◽  
Numerical Solutions ◽  
Singlet State ◽  
Numerical Calculations ◽  
Dimensional System ◽  
Dimensional Model ◽  
Yang Mills ◽  
Continuous And Discrete Spectra ◽  
New Construction ◽  
Discrete Spectra

Recent analytical and numerical solutions of above systems are reviewed. Discussed results include: a) exact construction of the supersymmetric vacua in two space-time dimensions, and b) precise numerical calculations of the coexisting, continuous and discrete, spectra in the four-dimensional system, together with the identification of dynamical supermultiplets and SUSY vacua. New construction of the gluinoless SO (9) singlet state, which is vastly different from the empty state, in the ten-dimensional model is also briefly summarized.

Geometry of Quantum States

2006 ◽  
Author(s):  
Ingemar Bengtsson ◽  
Karol Zyczkowski
Keyword(s):  
Quantum States
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