Saturday 31 October 2015

quantum mechanics - Momentum of wave function with sum of cosines


I am struggling with question about possible outcomes of momentum measurement and their probability. I know I can calculate it with momentum operator, but a wavefunction is of form


$$\psi (x)=3\cos\pi x+\cos3\pi x$$


and I am unsure how to deal with it, as the derivative consists of sines.


I know that $\cos{kx}=\frac{e^{ikx}+e^{−ikx}}{2}$ and $p_{x}=\hbar k$, but does it mean that the momentum is sum of eigenvalues of individual exponentials?




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