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This document discusses the algebraic approach to solving the simple harmonic oscillator (SHO) Hamiltonian. It begins by rewriting the SHO Hamiltonian in terms of creation and annihilation operators â and â†. This factorizes the Hamiltonian as the product of ↠and â up to an additive constant, with the number operator N̂ defined as â†â. The factorization allows important conclusions about the energy spectrum and ground state to be directly derived, including that energy eigenvalues must be greater than or

Author

Jeferson

Language

EN