2. Assume a Bohr hydrogen atom is in a superposition of the first two states, in which each has its usual definition = a +b√₂ You may assume that a and b are both real and positive. (a) What values of a and b will properly normalize the wave function and give probabilities of being found in the first and second states of 75% and 25%, respectively? (b) What will be the expectation value for the energy in this case? [eV] (c) What will be the standard deviation for this case? [eV]
2. Assume a Bohr hydrogen atom is in a superposition of the first two states, in which each has its usual definition = a +b√₂ You may assume that a and b are both real and positive. (a) What values of a and b will properly normalize the wave function and give probabilities of being found in the first and second states of 75% and 25%, respectively? (b) What will be the expectation value for the energy in this case? [eV] (c) What will be the standard deviation for this case? [eV]
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![2. Assume a Bohr hydrogen atom is in a superposition of the first two states, in which each has
its usual definition
You may assume that a and b are both real and positive.
(a) What values of a and b will properly normalize the wave function and give probabilities
of being found in the first and second states of 75% and 25%, respectively?
(b) What will be the expectation value for the energy in this case? [eV]
(c) What will be the standard deviation for this case? [eV]
(d) Demonstrate numerically that if I make three measurements at the first energy level
and one at the second, the standard deviation relative to the answer in (a) matches the
answer in (b).
Hint: you don't need to worry about any of the details of the wavefunctions. All you need
to know is that they're properly normaized and they're eigenfunctions of energy, with energy
levels of the Bohr atom that we discussed in class.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F831851de-f673-41f5-9f36-80ab878b6fd6%2Ffaf5ec7c-fea3-4c33-a1f6-321c5822d85c%2Fkvoz7_processed.png&w=3840&q=75)
Transcribed Image Text:2. Assume a Bohr hydrogen atom is in a superposition of the first two states, in which each has
its usual definition
You may assume that a and b are both real and positive.
(a) What values of a and b will properly normalize the wave function and give probabilities
of being found in the first and second states of 75% and 25%, respectively?
(b) What will be the expectation value for the energy in this case? [eV]
(c) What will be the standard deviation for this case? [eV]
(d) Demonstrate numerically that if I make three measurements at the first energy level
and one at the second, the standard deviation relative to the answer in (a) matches the
answer in (b).
Hint: you don't need to worry about any of the details of the wavefunctions. All you need
to know is that they're properly normaized and they're eigenfunctions of energy, with energy
levels of the Bohr atom that we discussed in class.
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