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[XMP/QM-13001] Short Examples --- Nature of Energy SpectrumNode id: 6327page$\newcommand{\sech}{\rm sech}$
We give several examples to explain how to obain the nature of energy spectrum without solving the problem completely. |
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24-07-11 17:07:31 |
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[NOTES/QM-13009] Delta Function Potential --- An overviewNode id: 6335pageAn 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 |
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[LECS/QM-ALL] Quantum Mechanics --- No Frills LecturesNode id: 5874collectionAbout this collection:
This is a collection of Lecture Notes on Quantum Mechanics.
An effort is made to keep the content focused on the main topics.
There is no discussion of related topics and no digression into unnecessary details.
Who may find it useful:
Any one who wants to learn or refresh all topics in standard two semester Quantum Mechanics course.
Topics covered:
The list of topics covered appears in the main body of this page.
Click on any topic to see details and links to content pages.
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24-07-09 04:07:34 |
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MacrosNode id: 6333page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d#2^2}}\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial#1}{\partial #2}}\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$
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24-07-08 17:07:38 |
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[DOC/Latex/Macros] Freq-Used-MacrosNode id: 6231page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial#1}{\partial #2}}\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$
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24-07-08 14:07:01 |
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[NOTES/QM-13010] Dirac Delta Function Potential -Direct integration of the Schr\"{o}dinger equationNode id: 4756page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d #2^2}}\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial#1}{\partial #2}}\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$
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 |
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[SCN/QM-13001] Reflection and Transmission Through a Square Barrier --- DetiailsNode id: 6330pageHere we give computational details of reflection and transmission coefficients for a beam incident on a square barrier. |
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24-07-07 08:07:45 |
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[NOTES/QM-13007] Particle in A Box Node id: 4751page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$
We derive the energy eigenvalues and eigenfunctions of a particle in a box of size \(L\). |
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24-07-07 07:07:15 |
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[NOTES/QM-13006] Boundary condition at a rigid wallNode id: 4750page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial#1}{\partial #2}}\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$
We derive the boundary condition on a rigid wall as a limit of the boundary condition on a the wave function at a point where the potential has a finite jump discontinuity. It is shown that there is no restriction on the derivative of the energy eigenfunction. The only boundary condition is that the eigenfunction must vanish. |
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24-07-07 07:07:40 |
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[NOTES/QM-13005] Reflection and Transmission from a PotentialNode id: 6328pageThe reflection and transmission coefficients for a potential problem in one dimension are defined. For this purpose it is sufficient to know the behavior of the wave function at large distances. To set up the problem one needs to impose a suitable boundary condition on the wave function at large distances. It is shown that, for real potentials, the probability conservation implies that the reflection and transmission coefficients add to unity.
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24-07-07 06:07:56 |
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QS 19: Rutherford scatteringNode id: 1148page$\newcommand{\dydxt}[2]{\frac{d#1}{d#2}}
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24-07-04 13:07:40 |
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QS 18: Born Approximation for a Central PotentialNode id: 1146page$
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24-07-04 13:07:03 |
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QS 17: Born SeriesNode id: 1145page[toc:0]
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24-07-04 13:07:19 |
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QS 16: Relativistic DecayNode id: 1156page[toc:0]
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24-07-04 13:07:44 |
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QS 15: Relativistic scatteringNode id: 1144page$
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24-07-04 13:07:07 |
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QS 14: Non-relativistic colliding beamsNode id: 1143page[toc:0]
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24-07-04 13:07:00 |
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QS 13: Momentum conservation : colliding beamsNode id: 1142page$
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24-07-04 13:07:05 |
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QS 12: Cross sections for non-relativistic potential scatteringNode id: 1141page$
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24-07-04 13:07:24 |
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QS 11: Plane wave = Beam of particles?Node id: 1140page\(\newcommand{\intp}{\int \frac{{\rm d}^3p}{2p^0}}
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24-07-04 13:07:38 |
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QS 10: Transition RateNode id: 1139page$\newcommand{\kk}[1]{|#1\rangle}
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24-07-04 13:07:44 |
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