Today, I happened to look into the term paper that I wrote for 8.06 (the third semester of Quantum Mechanics at MIT). I read it after almost 8 months, and was pleased to discover that I had written something that was clear and understandable.
The paper discusses how the Schrodinger spectrum of Hydrogen can be derived using the conserved Laplace-Runge-Lenz vector. I summarize the classical case, discuss Lie Algebras, derive the so(4) symmetry in Hydrogen and also calculate
1) the energy eigenvalues,
2) their degeneracy,
3) the permitted angular momentum values for a given energy state, and
4) the ground state wave function.
References are included in which the excited state wave-functions are constructed using ladder operators for so(4), and so(4) symmetry also holds in the relativistic Dirac Hamiltonian.
You can download and read the paper here.
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5 comments:
Raghu,
Went through the paper. It appears to be very well written, and I think that an attempt has been made to explain difficult mathematical concepts very lucidly.
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