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Evaluate the E expressions for both the Classical (continuous, involves integration) and the Quantum (discrete, involves summation) models for the energy density u, (v).

A particle with mass m is in the state .2 mx +iat 2h Y(x,t) = Ae where A and a are positive real constants. Calculate the expectation values of (x).

Consider the wavefunction Y(x) = exp(-2a|x|). a) Normalize the above wavefunction. b) Sketch the probability density of the above wavefunction. c) What is the probability of finding the particle in the range 0 < x s 1/a ?

Suppose a 1D quantum system is represented by the wavefunction in position space: (æ|2>(t)) = b(x, t) = Ae -3x+5it where it only exists () < x < ! Normalize the wavefunction, i.e., what is A?

The normalised wavefunction for an electron in an infinite 1D potential well of length 80 pm can be written:ψ=(0.587 ψ2)+(0.277 i ψ7)+(g ψ6). As the individual wavefunctions are orthonormal, use your knowledge to work out |g|, and hence find the expectation value for the energy of the particle, in eV.

A particle with the velocity v and the probability current density J is incident from the left on a potential step of height Uo, that is, U (x) = Uo at r > 0 and U(x) = 0 at r 0.