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- W28777636 abstract "A symmetrical treatment of the incoming and outgoing channels can be done in a basically very simple way by formulating the Schrodinger equation (1.1) in the form of a projection equation (see, e.g., ref. [WI 72]) $$ langle delta psi left| {{rm H} + frac{hbar }{i}frac{partial }{{partial t}}} right|psi rangle = 0 $$(2.1)As usual, the Dirac bracket denotes the integration over spatial coordinates and the summation over spin and isospin coordinates. If δΨ represents a completely arbitrary variation of Ψ at a given instant t in the complete Hilbert space, then eq. (2.1) implies that the vector $$ left( {{rm H} + frac{hbar }{i}frac{partial }{{partial t}}} right)left| {psi rangle } right. $$must be orthogonal to any arbitrary vector in this space. This evidently will be the case only if Ψ obeys eq. (1.1). Therefore, eq. (2.1) is merely another formulation of the time-dependent Schrodinger equation. However, as we shall see later, eq. (2.1) does allow us to treat the incoming and outgoing channels in a symmetrical way." @default.
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- W28777636 date "1977-01-01" @default.
- W28777636 modified "2023-09-24" @default.
- W28777636 title "Reformulation of the Schrödinger Equation" @default.
- W28777636 doi "https://doi.org/10.1007/978-3-322-85255-7_2" @default.
- W28777636 hasPublicationYear "1977" @default.
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