Consider a particle in the first excited state of an infinite square well of width L. This particle has wavefunction = √²/ sin (²7²) L √₂(x)= for -L/2 ≤ x ≤ L/2, and 2(x) = 0 elsewhere. a) What is the value of the energy of this particle, E₂? b) What is the probability density function, p, for this particle? c) At what values of a does the probability density vanish? d) What is the probability of finding this particle in the interval 0 ≤ x ≤ L/8?
Consider a particle in the first excited state of an infinite square well of width L. This particle has wavefunction = √²/ sin (²7²) L √₂(x)= for -L/2 ≤ x ≤ L/2, and 2(x) = 0 elsewhere. a) What is the value of the energy of this particle, E₂? b) What is the probability density function, p, for this particle? c) At what values of a does the probability density vanish? d) What is the probability of finding this particle in the interval 0 ≤ x ≤ L/8?
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Transcribed Image Text:Consider a particle in the first excited state of an infinite square well of width L. This particle has
wavefunction
*60 = √ (7)
4₂(x)
sin
L
for -L/2 ≤ x ≤ L/2, and 2(x) = 0 elsewhere.
a) What is the value of the energy of this particle, E₂?
b)
What is the probability density function, p, for this particle?
c) At what values of does the probability density vanish?
d)
What is the probability of finding this particle in the interval 0 ≤ x ≤ L/8?
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