ar X iv : 0 90 2 . 25 93 v 2 [ m at h - ph ] 4 S ep 2 00 9 1 Crum ’ s Theorem for ‘ Discrete ’ Quantum Mechanics
نویسنده
چکیده
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum’s theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral except for the lowest energy state. Its counterpart in ‘discrete’ quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schrödinger equation is a difference equation.
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