f(x + xo) = e' Pxo/h ƒ (x) (where xo is any constant distance). For this reason, §/ħ is called the genera- tor of translations in space. Note: The exponential of an operator is defined by the power series expansion: e = 1 + Ô + (1/2)Q² + (1/3!) Q³ + .... (b) If ¥(x, 1) satisfies the (time-dependent) Schrödinger equation, show that ¥(x,t + fo) = e-i Hto/h v (x. t) (where to is any constant time); –Ħ /ħ is called the generator of translations in time. ) Show that the expectation value of a dynamical variable Q(x, p, t), at time 1 + to, can be written³ 34 Use this to recover Equation 3.71. Hint: Let to = dt, and expand to first order in dt.

f(x + xo) = e' Pxo/h ƒ (x) (where xo is any constant distance). For this reason, §/ħ is called the genera- tor of translations in space. Note: The exponential of an operator is defined by the power series expansion: e = 1 + Ô + (1/2)Q² + (1/3!) Q³ + .... (b) If ¥(x, 1) satisfies the (time-dependent) Schrödinger equation, show that ¥(x,t + fo) = e-i Hto/h v (x. t) (where to is any constant time); –Ħ /ħ is called the generator of translations in time. ) Show that the expectation value of a dynamical variable Q(x, p, t), at time 1 + to, can be written³ 34 Use this to recover Equation 3.71. Hint: Let to = dt, and expand to first order in dt.