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### Why must the separation constant be real in a time dependent wave function?

I'm not sure if I'm asking this right. I'm reading ''Introduction to Quantum Mechanics'' by Griffiths and in the chapter 2 exercises he asks to prove that the separation constant, $E$, must be real. ...
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### Why Does the Dirac delta Function Fix the Normalization of the Basis Vectors in Infinite Dimensions? [duplicate]

On page 60 of Shankar's intro to QM at the very bottom he says that the Dirac delta function fixes the normalization of the basis vectors with an infinite amount of dimensions. I don't understand why ...
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### Inner product of standard-momentum one-particle states in Weinberg

My question has essentially already been addressed in Questions concerning some parts of the section on one-particle states in Weinberg's first volume on QFT (third question), but unfortunately ...
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### Help normalising and taking the inverse Fourier transform of this wavefunction [closed]

Normalising Consider the wavefunction $$\psi(x,0)=Ne^{-\frac{|x|}{\lambda}}.$$ In order to normalise this I take the integral, which due to the modulus on the $x$ I evaluate just from zero to ...
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### Normalization of a wave function in quantum mechanics

A more simple question, so I am watching a quantum mechanics lecture on potentials of free particles and am doing the general solution of schrodinger's stationary equation for a free particle when I ...
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### Normalized wave functions in position and momentum space

Using the following expression for the Dirac delta function: $$\delta(k-k')=\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(k-k')x}\mathrm{d}x$$ show that if $\Psi(x,t)$ is normalized at time $t=0$, ...
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### Free space propagator: reconciling two results

In quantum mechanics, the free space propagator $G(q_f=0,q_i=0;\tau)$ can be easily calculated to be $$\sqrt{\frac{m}{2\pi i \hbar \tau}}$$ by inserting an identity operator. However if we use ...
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### Normalizing a wave function in a mixed well

So I got this potential and want to solve for the even wavefunctions http://imgur.com/GKAy4nD Since it's symmetric around the origin I need only to look at the interval [0,b] and solve for the ...
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