# Questions tagged [normalization]

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### What is the physical meaning of the normalization of the propagator in quantum mechanics?

Suppose we have a quantum field theory (QFT) for a scalar field $\phi$ with vacuum state $|\Omega\rangle$. Then, in units where $\hbar = 1$, we postulate that the vacuum expectation value (VEV) of any ...
1 vote
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### Confusion on Shankar's Motivation for the Dirac delta Function

I was reading Shankar's Principles of Quantum Mechanics and got confused on page 60, where he motivates the delta function from the normalization problem of the inner product for function spaces. We ...
• 13
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### Discrete to continuous quantum operator

Let's say that we have a discrete lattice with $N$ sites. Let's label the site by the index $i$. Let's say that we have the operators $a_i$ and $a_i^\dagger$ which correspond to the creation and ...
• 665
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### Homogeneity of Schroedinger equation implies norm conservation

I am trying to understand how homogeneity of Schroedinger equation implies norm conservation. I know that we are considering the non-relativistic case, where particle number is conserved, so we do not ...
• 1,398
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### Square Integrability of spherical symmetric wave

In my class we were discussing some wave equation for a spherical symmetric wave $u(t,r)$ and my professor investigated the behaviour of the solutions asymptotics $r \rightarrow \infty$. The solution ...
• 753
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### Does the inner product of wavefunctions really have units? [closed]

Let $\psi(x)$ and $\phi(x)$ be wavefunctions. I usually see the inner product defined as $$\int dx\, \overline{\psi(x)} \, \phi(x)$$ and interpreted, I think, as "the amplitude that state $\phi$ ...
• 120
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### Non-normalizable eigenfunctions

I was reading Shankar's Principles of Quantum Mechanics when on page 65, he starts talking about infinite spaces and operators in them. He introduces an operator $K$, which in the $x$ basis takes the ...
• 129
1 vote
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### I don't understand the normalization of a quantum state in quantum machine learning paper

In the paper arXiv:1307.0411 by Seth Lloyd, Masoud Mohseni, Patrick Rebentrost on page 3, line 8, it says: Constructing the $\log_2N$ qubit quantum state $| v \rangle = |\vec{v}|^{-1/2}\vec{v}$ then ...
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