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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Consider a particle in a potential well U(x) that is initially in a state with
wavefunction 4(x, 0) and is an equal-weight superposition of the ground state
4o (x) and first excited state y, (x) wavefunctions:
Ψ(, 0)Α[ψ, (x) + ψ (x)]
(a) Show that A = ;
by normalizing Y(x, 0), assuming that ho and 41 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 Po and 41 are E, and E1 , respectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9bdb540a-50ee-4458-a770-17b9fda54b9c%2Feea784b5-5f68-476b-87cc-dd5310fd7998%2Fdkqicjr_processed.png&w=3840&q=75)
Transcribed Image Text:3.
Consider a particle in a potential well U(x) that is initially in a state with
wavefunction 4(x, 0) and is an equal-weight superposition of the ground state
4o (x) and first excited state y, (x) wavefunctions:
Ψ(, 0)Α[ψ, (x) + ψ (x)]
(a) Show that A = ;
by normalizing Y(x, 0), assuming that ho and 41 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 Po and 41 are E, and E1 , respectively.
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