Consider a particle in a potential well U(x) that is initially in a state with wavefunction Y(x, 0) and is an equal-weight superposition of the ground state 4o(x) and first excited state 4, (x) wavefunctions: Y(x, 0) = A[¥o(x) + ¥,(x)] (a) Show that A = by normalizing Y(x, 0), assuming that po and 4, are both normalized. (b) Determine and write Y(x, t) at any later time t. (c) Write the expressions for (E), (E²), and AE. Assume that the energy eigenvalues for , and y, are E, and E,, respectively.
Consider a particle in a potential well U(x) that is initially in a state with wavefunction Y(x, 0) and is an equal-weight superposition of the ground state 4o(x) and first excited state 4, (x) wavefunctions: Y(x, 0) = A[¥o(x) + ¥,(x)] (a) Show that A = by normalizing Y(x, 0), assuming that po and 4, are both normalized. (b) Determine and write Y(x, t) at any later time t. (c) Write the expressions for (E), (E²), and AE. Assume that the energy eigenvalues for , and y, are E, and E,, respectively.
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