Principle of stationary action in the Schrodinger representation

Before pursuing the variation of the atomic action integral, it is helpful to first recover the statement of the principle of stationary action in the Schrodinger representation for the total system. If one sets the boundary of the region Cl at infinity in eqn (8.118) to obtain the variation of the total system action integral 2 [ ] and restricts the variation so that ST vanishes at the time end-points and the end-points themselves are not varied, then only the terms multiplied by the variations in the first integral on the right-hand side remain. The Euler equation obtained by the requirement that this restricted 

Hermitian operator. It may be a function of the coordinates (inducing a gauge transformation) and/or of the momenta (inducing a translation of coordinates). If both sides of eqn (8.125) are divided by 2 — j and the result is subjected to the limit At 0, one obtains, to first-order, an expression for S UV, ], 

Equations (8.126) and (8.127) are identical in form to the corresponding results obtained for the variation of the Lagrange function operator in eqns (8.97) and (8.98). They are variational statements of the Heisenberg equation of motion for the observable F in the Schrodinger representation. When T describes a stationary state 

for a stationary state with a normalized state function eqn (8.127) assumes the form 

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