(1) A particle of mass m in the potential V(x) = \frac Λ {1}{2}m\omega ^{2}x^{2} has the initial wave function: \ Psi(x, 0) Ae^{\beta \xi ^{2}}. (a) Find out A. (b) Determine the probability that E_{0} = \hbar\omega/2 turns up, when a measurement of energy is performed. Same for E_{1} 3\hbar\omega/2. (c) What energy values might turn up in an energy measurement? [ Notice that many n values are ruled out, just as in your answer to (b).] (c) Sketch the probability to measure \
(1) A particle of mass m in the potential V(x) = \frac Λ {1}{2}m\omega ^{2}x^{2} has the initial wave function: \ Psi(x, 0) Ae^{\beta \xi ^{2}}. (a) Find out A. (b) Determine the probability that E_{0} = \hbar\omega/2 turns up, when a measurement of energy is performed. Same for E_{1} 3\hbar\omega/2. (c) What energy values might turn up in an energy measurement? [ Notice that many n values are ruled out, just as in your answer to (b).] (c) Sketch the probability to measure \
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![(1) A particle of mass m in the potential V(x) = \frac
{1}{2}m\omega^{2}x^{2} has the initial wave function: \
Psi(x, 0) Ae^{\beta \xi ^{2}}. (a) Find out A. (b)
Determine the probability that E_{0} = \hbar\omega/2
turns up, when a measurement of energy is performed.
Same for E_{1} 3\hbar\omega/2. (c) What energy
values might turn up in an energy measurement? [
Notice that many n values are ruled out, just as in your
answer to (b).] (c) Sketch the probability to measure \
hbar\omega/2 as a function of and explain the
maximum any calculation? why is it expected to be
there, even without performing](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7581e468-63b3-4b72-b638-c3bd3f01ed2a%2F06eb15a0-9851-4155-8b63-06339edff7ec%2Ftq7zk3e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(1) A particle of mass m in the potential V(x) = \frac
{1}{2}m\omega^{2}x^{2} has the initial wave function: \
Psi(x, 0) Ae^{\beta \xi ^{2}}. (a) Find out A. (b)
Determine the probability that E_{0} = \hbar\omega/2
turns up, when a measurement of energy is performed.
Same for E_{1} 3\hbar\omega/2. (c) What energy
values might turn up in an energy measurement? [
Notice that many n values are ruled out, just as in your
answer to (b).] (c) Sketch the probability to measure \
hbar\omega/2 as a function of and explain the
maximum any calculation? why is it expected to be
there, even without performing
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Step 1: Use of Normalization condition
VIEWStep 2: Calculation of probability integral for measurement of energy E0.
VIEWStep 3: Calculation of probability integral for measurement of energy E1.
VIEWStep 4: The energy values that only turn up when we do the energy measurement on given initial state.
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