A particle of mass m is in a one dimensional well of potential [itex]V(x)=\infty, |x| \geq a[/itex] and [itex]V(x)=0, |x| <a[/itex](adsbygoogle = window.adsbygoogle || []).push({});

(i) show the allowed energy eigenvalues are given by

[itex]E_n = \frac{\hbar \pi^2 n^2}{8ma^2}, n=1,2,...[/itex]

and determine the normalised eigenfunction [itex]u_n(x)[/itex]

then sketch the ground state wavefunction.

DONE THIS BIT

(ii)Suppose at t=0, the particle has a wavefunction described by

[itex]\psi(x)=0, |x|>a[/itex] and [itex]\psi(x)=N(a^2-x^2), |x| \leq a [/itex]

calculate the normalisation constant N and sketch the wavefunction

(iii)calculate the expectation value of the energy of the particle in state [itex]\psi[/itex] in (ii)

(iv)for the wavefunciton [itex]\psi[/itex] in (ii), what is the probability that a measurement of energy will yield a value corresponding tot eh ground state.

interpret your answer.

So i've done (i) i need someone to leas me through the rest of the questions please.

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# Quantum Question

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