a particle of mass m is confined in a infinite potential well that is centered on x o convince y

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Question

A particle of mass m is confined in an infinite potential well that is centered on x = 0. Convince yourself that the correct way to write the ground state wave function and the first excited state wave function is how they are written to the left. |x < a/2 = |Ïˆâ‚> cos(kx) < a/2 + sin(kx) > a/2 = |Ïˆâ‚‚> a) Do these have the expected energies? b) Suppose you have a wave function given by the symmetric "tent" wave function sin(2kx) < a/2 + sin(kx) > a/2 = |Ïˆâ‚ƒ> Î¨â‚ƒ(x) = (1/âˆša) * (sin(2kx) + sin(kx)) What is the probability that a measurement of the energy will give the ground state energy Eâ‚? c) What is the probability that a measurement of the energy will give the first excited state energy Eâ‚‚? Hint: you can do the integral for this one by inspection.

          A particle of mass m is confined in an infinite potential well that is centered on x = 0. Convince yourself that the correct way to write the ground state wave function and the first excited state wave function is how they are written to the left.
|x < a/2 = |Ïˆâ‚>
cos(kx) < a/2 + sin(kx) > a/2 = |Ïˆâ‚‚>
a) Do these have the expected energies?
b) Suppose you have a wave function given by the symmetric "tent" wave function
sin(2kx) < a/2 + sin(kx) > a/2 = |Ïˆâ‚ƒ>
Î¨â‚ƒ(x) = (1/âˆša) * (sin(2kx) + sin(kx))
What is the probability that a measurement of the energy will give the ground state energy Eâ‚?
c) What is the probability that a measurement of the energy will give the first excited state energy Eâ‚‚? Hint: you can do the integral for this one by inspection.

a particle of mass m is confined in a infinite potential well that is centered on x o convince yourself that the correct way to write the ground state wave function and the first excited sta 38655

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