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[NOTES/QM-13004] General Properties of Motion in One Dimension$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$ A discussion of nature of energy eigenvalues and eigenfunctions are discussed for general potentials in one dimension. General conditions when to expect the energy levels to be degenerate, continuous or form bands are given. Also the behaviour of eigenfunctions under parity and for also for large distances etc. are discussed. |
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24-07-17 05:07:46 |
[CHAT/QM-13002] LET's TALK --- NATURE OF ENERGY SPECTRUMFor a potential problem in one dimension there are three types of energy levels. These are (a) discrete, (b) continuous doubly degenerate energy eigenvalues, and (c) continuous and non degenerate. In this talk we explain the thumb rules to find out which of this cases apply for a given potential and a specified energy value. |
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24-07-17 04:07:26 |
[NOTES/QM-13009] Delta Function Potential --- An overviewAn overview of three methods to compute the energies and eigenfunctions of an attractive Delta function potential are given. |
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24-07-09 05:07:09 |
[NOTES/QM-13010] Dirac Delta Function Potential -Direct integration of the Schr\"{o}dinger equation$\newcommand{\DD}[2][]{\frac{d^2 #1}{d #2^2}}\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial#1}{\partial #2}}\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$ The energy eigenfunctions and eigenvalues for a particle in delta function potential are derived. It is found that, for an attractive delta function potential there is only one bound state. |
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24-07-08 06:07:34 |
[NOTES/QM-13001] Square Well Energy Eigenvalues and EigenfunctionsThe energy eigenvalue problem for a particle in a square well is solved. The energy eigenvalues are solutions of a transcendental equation which can be solved graphically. |
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24-07-04 05:07:55 |
[CHAT/SM-04001] Systems in Equilibrium with a Heat Reservoir |
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24-06-30 04:06:49 |
[CHAT/CM-08007] Let's Talk --- Fundamental InteractionsA short discussion of pseudo forces and fundamental interactions is given. |
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24-06-30 04:06:38 |
[TALK/CM-06001] Let's Talk --- Scattering |
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24-06-27 19:06:48 |
[TALK/CM-06002] Let's Talk --- Potential Scattering |
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24-06-27 19:06:24 |
[NOTES/QM-12003] Propagator for Free Particle$\newcommand{\Prime}{{^\prime}} \newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}} \newcommand{\xbf}{{\mathbf x}}$ The Green function and the propagator for time dependent Schr\:{o}dinger equation are defined. The time dependent Schr\"{o}dinger equation is soled to obtain the solution for propagator. |
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24-06-24 17:06:48 |