Requesting help with a physics problem

[John Chang]

I can't seem to get the right answer, so I thought I'd ask, beg or borrow a clue from someone here on how you get the right answer to this problem.

44. The energy eigenstates for a particle of mass m
in a box of length L have wave functions
fn(x) = 2/Lsin(npx/L) and energies
En =n^2(pi^2)(h-bar)^2/2m(L^2), where n = 1, 2, 3, . . . .
At time t = 0, the particle is in a state described
as follows.

psi = 1/sqrt(14) [f1 + 2*f2 + 3*f3]

Which of the following is a possible result of a
measurement of energy for the state Y ?
(A) 2E1
(B) 5E1
(C) 7E1
(D) 9E1
(E) 14E1

As I review, - (h-bar)^2/2m * d^2/dx^2(psi) - E*psi = 0, for this particular case. Or E = - h-bar^2/2m * (psi''/psi)?

I seem to go off in the weeds when I try to find E by taking the 2nd derivative of psi, is there a better way to calculate E, given a specific wavefunction for a particle in a box?

 

[John G]

I can't seem to get the right answer, so I thought I'd ask, beg or borrow a clue from someone here on how you get the right answer to this problem.

44. The energy eigenstates for a particle of mass m
in a box of length L have wave functions
fn(x) = 2/Lsin(npx/L) and energies
En =n^2(pi^2)(h-bar)^2/2m(L^2), where n = 1, 2, 3, . . . .
At time t = 0, the particle is in a state described
as follows.

psi = 1/sqrt(14) [f1 + 2*f2 + 3*f3]

Which of the following is a possible result of a
measurement of energy for the state Y ?
(A) 2E1
(B) 5E1
(C) 7E1
(D) 9E1
(E) 14E1

As I review, - (h-bar)^2/2m * d^2/dx^2(psi) - E*psi = 0, for this particular case. Or E = - h-bar^2/2m * (psi''/psi)?

I seem to go off in the weeds when I try to find E by taking the 2nd derivative of psi, is there a better way to calculate E, given a specific wavefunction for a particle in a box?

I'm much better at finding people who know physics than actually knowing physics so um... try this:

http://www.physicsforums.com/showthread.php?t=99643

 

[ark]

En =n^2(pi^2)(h-bar)^2/2m(L^2), where n = 1, 2, 3, . . . .
At time t = 0, the particle is in a state described
as follows.

psi = 1/sqrt(14) [f1 + 2*f2 + 3*f3]

Which of the following is a possible result of a
measurement of energy for the state Y ?
(A) 2E1
(B) 5E1
(C) 7E1
(D) 9E1
(E) 14E1

First note that En=n^2 E1

Now 1^2 E1= E1
2^2 E1 = 4E1 (for f2)
3^2 E1 = 9E1 (for f3)

Therefore, only (D) can be a possible result for psi out of those listed. All other information is unnecessary.

Added: In fact, it is not a quantum theory problem. It is a simple intelligence test disguised as a quantum theory problem!

 

[John Chang]

En =n^2(pi^2)(h-bar)^2/2m(L^2), where n = 1, 2, 3, . . . .
At time t = 0, the particle is in a state described
as follows.

psi = 1/sqrt(14) [f1 + 2*f2 + 3*f3]

Which of the following is a possible result of a
measurement of energy for the state Y ?
(A) 2E1
(B) 5E1
(C) 7E1
(D) 9E1
(E) 14E1

First note that En=n^2 E1

Now 1^2 E1= E1
2^2 E1 = 4E1 (for f2)
3^2 E1 = 9E1 (for f3)

Therefore, only (D) can be a possible result for psi out of those listed. All other information is unnecessary.

Added: In fact, it is not a quantum theory problem. It is a simple intelligence test disguised as a quantum theory problem!

D'oh! You're right - the only energy values it can take are the n^2E1 values - anything else is meaningless. Ok, now that makes sense.