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6. Orthonormality of Infinite Square Well States. Prove that the eigenstates of the particle in the infinite square well are orthonormal to one another. That is, prove that if the box extends from $x = 0$ to $x = L$, the wave functions $psi_n(x)$ satisfy $int_0^L psi_n^*(x)psi_m(x)dx = delta_{nm}$ (5) Here, $delta_{nm}$ is the Kronecker-delta function. It is equal to 0 if $n eq m$ and 1 if $n = m$. Since the wavefunctions are normalized by construction, it is sufficient to demonstrate only the case when $n eq m$ in order to complete the proof. Hint: You may find it easiest to use Euler's identity to write the wavefunction in terms of complex exponentials, using the results from problem 1, and thereby simplifying the integrations.

          6. Orthonormality of Infinite Square Well States.
Prove that the eigenstates of the particle in the infinite square well are orthonormal to one
another. That is, prove that if the box extends from $x = 0$ to $x = L$, the wave functions
$psi_n(x)$ satisfy

$int_0^L psi_n^*(x)psi_m(x)dx = delta_{nm}$

(5)

Here, $delta_{nm}$ is the Kronecker-delta function. It is equal to 0 if $n 
eq m$ and 1 if $n = m$. Since the
wavefunctions are normalized by construction, it is sufficient to demonstrate only the case
when $n 
eq m$ in order to complete the proof. Hint: You may find it easiest to use Euler's
identity to write the wavefunction in terms of complex exponentials, using the results from
problem 1, and thereby simplifying the integrations.

6. Orthonormality of Infinite Square Well States.
Prove that the eigenstates of the particle in the infinite square well are orthonormal to one
another. That is, prove that if the box extends from x = 0 to x = L, the wave functions
psin(x) satisfy

int0^L psin^*(x)psim(x)dx = deltanm

(5)

Here, deltanm is the Kronecker-delta function. It is equal to 0 if n
eq m and 1 if n = m. Since the
wavefunctions are normalized by construction, it is sufficient to demonstrate only the case
when n
eq m in order to complete the proof. Hint: You may find it easiest to use Euler's
identity to write the wavefunction in terms of complex exponentials, using the results from
problem 1, and thereby simplifying the integrations.

Added by Nicholas H.

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