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DYK-12 :: What is a gauge? as Explained by Pankaj SharanNode id: 3103page
The following (from notes for a lecture I was preparing) might help explain the context: The first gauge theory was Hermann Weyl's extension of Einstein's general theory of relativity with a parallel transport that can change the scale or 'gauge' of lengths of the transported vector. About this one can read in P. G. Bergman's book on Relativity. The Hamiltonian formulation of electrodynamics, and in particular, the replacement of \(\vec{p}\) by \(\vec{p}-e\vec{A}/c \) was given by Larmor in his book "Aether and Matter", Cambridge (1900). [quoted by Pauli in ''General Principles of Quantum Mechanics" , Section 4. (Tr. by P. Achuthan and K. Venkatesan of 1958 German edition) Allied, New Delhi 1980.] In quantum mechanics the 'canonical momentum' \(\vec{p}-e\vec{A}/c\) becomes \(-i\hbar[\nabla-ie\vec{A}/(\hbar c)]\). The gauge invariance of the Schrodinger theory under \(\vec{A}\to \vec{A}+\nabla f\) and \(\phi\to \phi-(e/c)\frac{\partial f}{\partial t} \) when \(\Psi\) is changed by a phase was first given by V. Fock (1927). The analogy of this group of transformations to the Weyl theory on gravitation and electricity was pointed out by F. London (1927). The connection of this group to charge conservation was pointed out by Weyl while writing variational principle for the wave equation. [See Pauli as above.]
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DYK-10 Schrodinger was never comfortable with quantum jumpsNode id: 2962page |
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EM-Theory :: Facts to be RememberedNode id: 2928page |
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Quantum Mechanics :: Facts to be Remembered Node id: 2236page Content Under Development
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PTR/EM-04001 Properties of ConductorsNode id: 2235page |
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DYK-08 Who proposed electron spin first and what happened to the proposal?Node id: 2114page |
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PTR/QM-06003 --- Probabilty and average value Node id: 1970page |
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PTR/QM-06002 --- Dynamical Variables as hemitian operators Node id: 1969page |
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PTR/QM-06001 --- States of a quantum system Node id: 1968page |
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DYK-07 How good is Newtonian mechanics for planetary motion? Node id: 1899page |
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DYK-06 Position Operator in Relativistic Quantum Mechanics Node id: 1831page |
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DYK-05 Change in Sign of Fermion Wave Function under 2$\pi$ RotationNode id: 1830pageIt is well known the wave function of a fermion changes sign under rotation by \(2\pi\). Has this been verified experimentally?
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DYK-04 Who Revived the Klein Gordon Equation?Node id: 1828pageThe Klein Gordon equation in its original interpretation suffered from problem of negative probabilities. After quantum electrodynamics was successfully formulated, the second quantized Klein Gordon equation was shown to give a consistent formulation for spin zero particles. WHO DID THIS WORK?
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DYK-03 Jacobi Action PrincipleNode id: 1827pageJacobi Action Principle
A Second Variational Principle for Conservative Systems
Hamilton.'s action principle in classical mechanics is widely taught. There is a lesser known, but important Jacobi principle which is like Fermat's principle for waves. This form of action principle was used by Schrodinger to arrive at his hafous equation for qunatum mechanics of a point particles.
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DYK-02 Connection beteen Keplers and Hooke's force laws Node id: 1826pageCoulomb's force law and Hooke's law are connected by a transformation called Bohlin's transformation.
$\newcommand{\DD}[2][]{\frac{d^2#1}{d#2^2}}$
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Random Mix-06 An example of Quantum Effects in Stars Node id: 851pageAn example of Quantum Effects in Stars
Sarita Vig
Department of Earth and Space Sciences
Indian Institute of Space Science and Technology (IIST)
Valiamala, Tiruvananthpuram 695547, INDIA
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Works of Masters always have something to offerNode id: 723pageI take the best from every one. But GOLD FROM OLD,
There is always something to learn from MASTERS;
In this age of internet, there is a tendency to open internet and learn from Wikipedia and similar sites. While this has its own advantages for a mature learner, I recommend that a beginner must learn from the masters even though the learning curve may look very steep.
This collection is an attempt to encourage younger generation to leart role of contibuting to the subject and from the very best.
There are many who contributed to pedgogy and teaching. Many old texts become 'obsolete' simply because is it fashionable to go for the latest. It would be foolhardy to ignore these and other works, so we include here snippets and quotes etc. from many other sources too.
It is hoped this will provide incentive to the younger generations to ask for more.
"Choose the very best from every one"
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Sample Grading by CategoryNode id: 290page |
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Sample Rapid Fire QuizNode id: 288page |
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Sample Quiz : Identities in QM Node id: 286page |
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