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# Consider the harmonic oscillator wave function 1/4 where α = (-)"*. Here k, is the stiffness...

## Question

###### Consider the harmonic oscillator wave function 1/4 where α = (-)"*. Here k, is the stiffness...

Consider the harmonic oscillator wave function 1/4 where α = (-)"*. Here k, is the stiffness coefficient of the oscillator and m is mass. Recall that the oscillation frequency iso,s:,k, / m In class we showed that Ψ0(x) Is an eigenfunction of the Hamiltonian, with an eigenvalue Eo (1/2)ha a) Normalize the wave function in Eq.(1) b) Graph the probability density. Note that a has units of length and measures the "width" of the wave function. It's easier to use x/a in labeling the x-axis. c) Calculate the uncertainty in x. Ar=kr>-<i> . Leave your answers in terms o d) Calculate the uncertainty in p, Ap= p>-<p> e) Show that the uncertainty principle is satisfied. , -ba 2b Hints. (16x dx = π / b x e ax 2b

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