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### How do we normalize a delta function position space wave function? [duplicate]

I have a position space wavefunction $$\psi(x) = \delta(x-a) + \delta(x+a).$$ Now the question states to compute the following: The Fourier transform of $\psi(x)$. (Which invariably is the momentum ...
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### Hilbert space of harmonic oscillator: Countable vs uncountable?

Hm, this just occurred to me while answering another question: If I write the Hamiltonian for a harmonic oscillator as $$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$ then wouldn't one set of ...
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In Griffiths Introduction to Quantum Mechanics on page 102 it is shown, that the eigenfunctions of the position operator $\hat{x}=x$ are not normalizable. $$\int_{-\infty}^{\infty}g_{\lambda}\left(x\... 2answers 494 views ### Weyl anomaly in 2d CFT (string theory lectures by D.Tong) In his lectures on String Theory (http://www.damtp.cam.ac.uk/user/tong/string.html), Tong gives a proof of the Weyl anomaly, using equation (4.36). It seems wrong to me. Here he uses the OPE ... 4answers 329 views ### Having trouble understanding some stuff about delta functions [closed] I was going through one of the examples in Griffith's Quantum book and there was a few things in Example 3.3 that I didn't understand that I was hoping to get some clarification on. For instance, we ... 1answer 964 views ### Getting rid of double delta function in Feynman rules [1] A very simple example of feynman rule for scalar fields. After computing the diagram i have got the following:$$ -i(2\pi)^4g^2\int d^4q \frac{i}{q^2 -m^2c^2}\delta^{(4)}(p_1 - p_3 -q) \...
I have come across the expression $$\int f(x) \delta(x-a) \delta''(x-a) \mathrm dx$$ where the prime represents the derivative. Usually with derivatives of the delta distribution I'd partially ...