- #1
tanaygupta2000
- 208
- 14
- Homework Statement
- A quantum particle is confined in a one-dimentional box defined by the potential,
V{x) = 0 for 0 < x < L, and infinity otherwise. The particle is in the ground state. What is the
probability (P+) that an experimenter will find it moving along the positive-x direction?
What would be the magnitude of momentum (p) of that motion?
(a) P+ = 0 and p = 0
(b) P+ = 1/2 and p=n/L
(c) P+=1/2Landp=n/L
(d) P+ = 1/2 and p = 0
(e) P+ = 0 and p = 1t / L
- Relevant Equations
- wave function, psi = sqrt(2/L) sin(pi x/L)
Energy,E = pi^2 hbar^2/2mL^2
For the region where V = 0, solving the schrodinger equation leads to the above value of wave function, psi = sqrt(2/L) sin(pi x/L)
Since in the qus. it is not stated about the 'direction of movement' only restricted to +x direction, I think that the probability will be 1/2.
And finding the expectation value of momentum for this wave function, i am getting something like -i hbar/2L, which is nearly equal to 0.
So, I think that the correct option will be option-(d).
Am I right? Help will be appreciated!
Since in the qus. it is not stated about the 'direction of movement' only restricted to +x direction, I think that the probability will be 1/2.
And finding the expectation value of momentum for this wave function, i am getting something like -i hbar/2L, which is nearly equal to 0.
So, I think that the correct option will be option-(d).
Am I right? Help will be appreciated!