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In theoretical physics, the superpotential is a parameter in supersymmetric quantum mechanics. ==An example of superpotentiality== Consider a one-dimensional, non-relativistic particle with a two state internal degree of freedom called "spin". (This is not quite the usual notion of spin encountered in nonrelativistic quantum mechanics, because "real" spin applies only to particles in three-dimensional space.) Let ''b'' and its Hermitian adjoint ''b''† signify operators which transform a "spin up" particle into a "spin down" particle and vice versa, respectively. Furthermore, take ''b'' and ''b''† to be normalized such that the anticommutator equals 1, and take that ''b''2 equals 0. Let ''p'' represent the momentum of the particle and ''x'' represent its position with ()=i, where we use natural units so that . Let ''W'' (the superpotential) represent an arbitrary differentiable function of ''x'' and define the supersymmetric operators ''Q''1 and ''Q''2 as : : Note that ''Q''1 and ''Q''2 seem self-adjoint. Let the Hamiltonian be : where ''W signifies the derivative of ''W''. Also note that =0. Under these circumstances, the above system is a toy model of ''N''=2 supersymmetry. The spin down and spin up states are often referred to as the "bosonic" and "fermionic" states, respectively, in an analogy to quantum field theory. With these definitions, ''Q''1 and ''Q''2 map "bosonic" states into "fermionic" states and vice versa. Restricting to the bosonic or fermionic sectors gives two partner potentials determined by : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「superpotential」の詳細全文を読む スポンサード リンク
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