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A particle of mass m is in the state:

Ψ (x, t) = Aexp[-a(sqrt (mx^2) / h)-i (at / sqrt(m )) ]

where A and a are positive real constants.

a) Determine A.

b) What is the frequency ƒ associated with the wave function of this particle?

Explain your reasoning.

c) For what potential energy function U(x), does Ψ satisfy the Schrödinger

equation?

d) If we use the interpretation of [Ψ(x)]^2 dx as the probability that a particle of

mass m can be found in a region of width dx around the position x,

calculate the expected value (average value) of the position x.

Many thanx

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# Homework Help: Wave function

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