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bhaswati
physical explanation of accidental degenaracy
what type of symmetry?? i mean for hydrogen atom,the energy eigen values are degenerate w.r.t l i.e,potential is central i.e,v(r)=-1/r^m.why it is called accidental??
The radial symmetry of the potential gives you the degeneracy in m, which is "expected." The additional symmetry that produces the "accidental" (unexpected) degeneracy in l is conservation of the Lenz vector:\[{\bf p} \times {\bf L} - \frac{1}{r} {\bf r}\]Roughly speaking, it's the fact that in a 1/r potential the direction of an elliptical orbit does not change.