(I) Suppose the wave function for an electron at time t = 0 is given by (r,0) V2/L sin(5Tx/L). Which one of the following is the wave function at time t? (a) v(x, t) = Vt sin(5mx/L) cos(E,t/h) (b) v(x, t) = VZ sin(57x/L)e¬iEst/h (c) Both (a) and (b) above are appropriate ways to write the wave function. (d) None of the above. (II) The wave function for an electron at time t = 0 is given by (x,0) Vi sin(57x/L). Which one of the following is true about the probability density, (r,t)², after time t? (a) b(r, t)² = } sin?(57x/L) cos (Est/h). (b) |Þ(x, t)? = Z sin?(57x/L)e¬i2Est/h. (c) (r, t)² = } sin (57x/L) which is time-independent. . (d) None of the above.
(I) Suppose the wave function for an electron at time t = 0 is given by (r,0) V2/L sin(5Tx/L). Which one of the following is the wave function at time t? (a) v(x, t) = Vt sin(5mx/L) cos(E,t/h) (b) v(x, t) = VZ sin(57x/L)e¬iEst/h (c) Both (a) and (b) above are appropriate ways to write the wave function. (d) None of the above. (II) The wave function for an electron at time t = 0 is given by (x,0) Vi sin(57x/L). Which one of the following is true about the probability density, (r,t)², after time t? (a) b(r, t)² = } sin?(57x/L) cos (Est/h). (b) |Þ(x, t)? = Z sin?(57x/L)e¬i2Est/h. (c) (r, t)² = } sin (57x/L) which is time-independent. . (d) None of the above.
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Transcribed Image Text:(III) Now suppose that the wave function for an electron at time t = 0 is given by (x, 0) = A sin (Tx/L)
where A is a suitable normalization constant. Which one of the following is the wave function at time t?
(a) p(x, t) = A sin°(Tx/L) cos (Est /h)
(b) Þ(x, t) = A sin°(rx /L)e-iEst/ħ
(c) Both (a) and (b) above are appropriate ways to write the wave function.
(d) None of the above.
(IV) The wave function for an electron at time t = 0 is given by (x,0) = A sin°(rx/L) where A is a
suitable normalization constant. Which one of the following is true about the probability density |(x, t)|²
after time t?
(a) Þ(x,t)P = [AP sin1º(7x/L) cos²(Est/ħ).
(b) W(x, t)² = |AP sin1º (7x /L)e¬i2Est/h.
(c) p(x, t)[² = |AP sin°(rx/L) which is time-independent.
(d) None of the above.
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Transcribed Image Text:(I) Suppose the wave function for an electron at time t = 0 is given by (x,0) = /2/L sin(57x/L).
Which one of the following is the wave function at time t?
(a) p(x, t) =
Vž sin(57x/L) cos(Est/h)
(b) p(x, t) =
Vž sin(57x/L)e-iEst/h
(c) Both (a) and (b) above are appropriate ways to write the wave function.
(d) None of the above.
(II) The wave function for an electron at timet =0 is given by (x,0) = /? sin(57x/L). Which one of
the following is true about the probability density, |p(x, t)², after time t?
(a) [h(x, t)* = { sin²(57x/L) cos²(Est/h).
(b) |Þ(x, t)P = Z sin?(57x/L)e¬i2Est/h.
(c) |Þ(x,t)[² = } sin (57x/L) which is time-independent.
(d) None of the above.
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