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Particle in a Box for State Particle

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Consider a particle of mass m in a box of length a. Assume the state of the particle at time t=0 is:

Where are the particle in a box stationary states with energy

a. What is the probability a measurement of the energy will result in
b. What is the expectation (average) value for the energy (<E>) in the state ?
c. What is the probability a single measurement will yield the value E=<E>?
d. Write down an expression for the time-dependent wavefunction for this state, , in terms of the mass of the particle and the length of the box?

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The eigenfunctions of the one dimensional particle in a box are orthonormal:
(1.1)
The associated energies are:
(1.2)
To measure certain energy the system must be in ...

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The expert examines the concepts of particle in a box for state particles.

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