(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a particle of mass m is in the groundstate of a 1D box with width a. the box then expands rapidly and symmetrically to width 2a. i). What is the probability that the particle is in the new groundstate immediately after the expansion? and ii). how rapid must this expansion be for your calculation to be valid?

2. Relevant equations

timescale for change must be hbar/ |E_alpha -E_ beta|

i think for probabilty you use that the statefunction evolves in time according to the Schrodinger equation and probabilty is the mod squared of the wave-function.

3. The attempt at a solution

- pre expansion i got the energy of the groundstate as h^2/8ma^2
- and after expansion h^2/32ma^2
- the wavefunction is SQRT(PI/2a) cos (PI.x/a) before and after the expansion.

for part ii). i got (3/64PI) * (ma^2/h) for how rapid the expansion must be

for part i). i am stuck! [We were given the hint to use the fourth postulate to compute the probability that given the state-function (above), a measurement of energy will give the ground state energy of the expanded box (which i worked out above). ]

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Quantum physics - time dependant changes

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