(a) Consider a wave function ( Psi(x, t)=left[A e^{frac{i p x}{hbar}}+B e^{-frac{i p x}{hbar}} ight] e^{-frac{i p^{2} t}{2 m hbar}} ). Find the probability current corresponding to this wave function. What is the implication of the term ( e^{-frac{i p^{2} t}{2 m hbar}} ). (b) Show that for a one-dimensional square integrable wave-packer ( int_{-infty}^{infty} j(x) d x=frac{langle p angle}{m} ) where ( j(x) ) is the probability current, ( mathrm{m} ) is the mass of the particle and ( <p> ) is the expectation value of the momentum.
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\[ \Psi(x, t) = \left[A e^{\frac{i p x}{\hbar}} + B e^{-\frac{i p x}{\hbar}}\right] e^{-\frac{i p^2 t}{2 m \hbar}} \] Show more…
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