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[QUE/QFT-01002]Node id: 4003pageCompute infinitesimal variations of the Lagrangian density for the Schrodinger field under the Galilean transformation \begin{equation} \vec{x} \longrightarrow \vec{x}{'} = \vec{x} + \vec{v} t \end{equation} and \begin{equation} \psi(\vec{x}) \longrightarrow \psi{'}(\vec{x}\,{'}) = e^{-im\vec{v}\,^{{'}\,2} t/(2\hbar)} e^{im\vec{v}\cdot\vec{x}/\hbar} \psi(\vec{x}). \end{equation} Verify that the the change in Lagrangian is a total time derivative. Find the corresponding constant of motion. |
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[NOTES/QM-25001] Electormagnetic WavesNode id: 4928page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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[NOTES/QM-25002] Approximating matter radiation interactionsNode id: 4929page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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[NOTES/QM-25003] Charged Particle in E.M. FieldNode id: 4931page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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[NOTES/QM-25004] Induced Emission and Absorption Node id: 4932page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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Equilibrium in Quantum ThermodynamicsNode id: 5323forum |
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[NOTES/QM-16010] Classical Motion in Three Dimensions Spherically symmetric potentialsNode id: 4802page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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[NOTES/QM-16009] Solving Spherically Symmetric Problems In Quantum MechanicsNode id: 4801page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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[NOTES/QM-16008] Spherically Symmetric Square WellNode id: 4800page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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[NOTES/QM-16007] Particle in a Rigid Spherical BoxNode id: 4799page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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[NOTES/QM-16006] Energy Levels in Spherically Symmetric Potentials Accidental DegeneracyNode id: 4792page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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[NOTES/QM-16004] Free Particle Solution in Polar CoordinatesNode id: 4783page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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[NOTES/QM-16003] Solution of Radial Equation for a Constant PotentialNode id: 4782page |
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[NOTES/QM-16002] Spherically Symmetric Potentials — Using Spherical Polar CoordinatesNode id: 4781page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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[NOTES/QM-17002] Addition of Angular Momenta — Statement of ProblemNode id: 4814page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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