11-qm-Symmetry

11-qm-Symmetry - Ch.11 Symmetries and their consequences...

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Unformatted text preview: Ch.11 Symmetries and their consequences Translation Invariance ; Parity Violation C.S. Wu (1912-1997) 1 2011 QM I (PHYS505) (B. I. Min) POSTECH C. N. YANG and T.-D. LEE 1957 Lagrange Eq. of motion 2 Hamilton’s Canonical Eq. Cyclic Coordinate 3 Poisson bracket Constants of Motion 4 Invariance & Conservation Invariance & Conservation 5 The Symmetries of the Hamiltonian Ch.2 If is solution, so is Canonical Transformation ; 6 ; : generator of the transformation Ex) ; 7 problem. 11.2. Translational Invariance in Quantum Theory : translated state QM 8 : translated state b Active Translation operator by ε. State vector Passive moving the passive Operator 9 the passive 10 Translational Invariance ; construct may Let us G : Generator (Hermitian) (T: unitary G : Generator (Hermitian) (T: unitary) Moment m is the generato 11 Momentum is the generator Momentum conservation from translational invariance Ehrenfest’s theorem Ehrenfest’s theorem : 12 So G=P Translational invariance & P) 13 Ehrenfest’s theorem....
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11-qm-Symmetry - Ch.11 Symmetries and their consequences...

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