Explicit Calculations for Anharmonic Oscillators Using Lie Algebras
نویسنده
چکیده
1. Algebraic Preliminaries 1 1.1. Normal Ordering and Weyl Binomial Coefficients 1 1.2. Baker-Campbell-Hausdorff and the Hadamard Lemma 2 1.3. The Formula Often Desired and Rarely Known 3 2. The Method of [JA] 3 3. Lie Algebras up to Order One in λ 5 4. Explicit Computations 6 4.1. Odd Powered Potentials 6 4.2. Even Powered Potentials 8 5. Extending the Method 10 5.1. Simple One Dimensional Corollaries 10 5.2. Simple N Dimensional Corollaries 11 5.3. Higher Order Perturbations 11 6. Discussion 13 Appendix: Dealing with Harmonic Oscillators 14 References 15
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