# Tagged Questions

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### Normalizing Propagators (Path Integrals)

In the context of quantum mechanics via path integrals the normalization of the propagator as $$\left | \int d x K(x,t;x_0,t_0) \right |^2 ~=~ 1$$ is incorrect. But why? It gives the correct pre-...
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### How to guarantee square integrable solutions to time-independent Schrödinger's equation?

Given the time-independent Schrödinger’s equation in one dimension $$H\psi = E\psi$$ what restrictions can we place on V(x) (inside the hamiltonian) and E to guarantee that the solutions won't have ...
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### Physical position eigenfunction normalisation

We know that the Dirac function $$\delta(a)=\lim_{a \rightarrow 0} \delta_{a}(x)$$ can be written as an infinitesimally narrow Gaussian: $$\delta_{a}(x) := \frac{1}{\sqrt{2\pi a^2}}e^{-x^2/2a^2}$$ ...
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### S-Matrix and normalization of states

I'm trying to understand what is the S-matrix in QFT. People say that it has to be a unitary matrix, but that I guess will change with a different normalization of the incoming and outgoing states. My ...
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### Hilbert space, does $|r\rangle$ satisfy $\langle r |r\rangle = 1$?

Let's say we start with no particles: $\mid0\rangle$. We have $\vec{p}\vert0\rangle = 0$, $H\vert0\rangle = 0$, where we are ignoring $\infty$ vacuum energy. Also, $a(\vec{k})\vert0\rangle = 0$ for ...
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### Why must these Spinors be normalized?

I have just begun studying spin and there are two spinors mentioned: The main spinor $\chi$ and the spin-up spin down spinors (eigenspinors) $\chi_+ ,\chi_-$. I learned that the main spinor is a ...
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### Who is doing the normalization of wave function in the time evolution of wave function?

In the Schrodinger equation, at any given time $t$ we should jointly add another sub equation, like $$||\psi_t(x)|| = 1$$ where $\psi_t(x) = \Psi(x,t)$, and then try to solve the two equations ...
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### Normalization of wave function meaning…?

I just have one question. I'm doing a problem where I'm told to normalize a wave function, which is split up into two regions, namely where $r \leq r_0$ and $r > r_0$. My question is, why am I ...
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### Expected value inequality

Why is $\langle p^2\rangle >0$ where $p=-i\hbar{d\over dx}$, (noting the strict inequality) for all normalized wavefunctions? I would have argued that because we can't have $\psi=$constant, but ...
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### What does the notation $\Psi_k/(\Psi_k,\Psi_k)^{1/2}$ mean?

I am currently reading the paper "Gravitation and quantum mechanics for macroscopic objects" by F. Karolyhazy (1966). In his paper, he uses certain notation that I haven't come across before (he also ...
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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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### Energy term in Wavefunction Normalization

I recently started learning quantum mechanics and when I solved the Schrödinger equation for the Hydrogen atom, in particular the Radial equation, I found that I had normalized it but a term in the ...
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### Why is the inner product of position eigenstates not normalised? [duplicate]

I have read that $$<{\bf r}|{\bf r}'> = δ({\bf r}-{\bf r}').$$ I don't understand how this is correct, I want to say it is equal to 1 or 0, rather than an unnormalised delta function. Clearly ...
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### Spin half for the value of $|1 0\rangle$?

Spin-1/2 The eigenspinor , $X=aX_++bX_-$ $$X_+=\left( \begin{array}{cc} 1\\ 0\end{array} \right)$$$$X_-=\left( \begin{array}{cc} 0\\ 1\end{array} \right)$$ They are define like this because they ...
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### Proper notation for normalized scalar?

I have not been able to find a resource to tell me the standard notation for a normalized scalar value. Normalized vectors (i.e. unit vectors) are typically denoted by placing a hat over the variable,...
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### Normalizable wave functions?

How can I test whether a wave function is normalizable? If you apply an operator to a wave function, sometimes the result will not be normalizable. But how can I find these wave functions that do not ...
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### How can we justify identifying the Dirac delta function with the eigenfunction of position? [duplicate]

I can think of at least two different ways to understand eigenfunctions of operators in quantum mechanics. But neither one seems to provide a good explanation for why we take the position-basis ...
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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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### Problem in understanding Feynman's explanation of the Dirac-Delta function [duplicate]

This is quoted from Feynman's Lectures' Normalization of the states in $x$: We return now to the discussion of the modifications of our basic equations which are required when we are dealing with ...
In Griffith's book, Introduction to Quantum Mechanics, in the equation:  \frac{\partial}{\partial t} \left| \Psi\right|^2 = \frac{i\hbar}{2m} \left( \Psi^* \frac{\partial^2 \Psi}{\partial x^2} - \...