Word Count : 334

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We are given that the wavefunction in position space is expressed as a Fourier transform of the momentum-space wavefunction: $$ \Psi(x,t) = \frac{1}{\sqrt{2\pi\hbar}} \int_{-\infty}^{\infty} e^{i(p_x x - E t)/\hbar} \Phi(p_x,t) \, dp_x $$ --- ### Step 1: Given that $\Psi(x,t)$ is normalized This means: $$ \int_{-\infty}^{\infty} |\Psi(x,t)|^2 \, dx = 1 $$ Our goal is to show that: $$ \int_{-\infty}^{\infty} |\Phi(p_x,t)|^2 \, dp_x = 1 $$ _______ ___ _______ ____ _____.
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