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### Express state as eigenkets

This is very basic but I just suddenly got confused. Any state can be expressed as complete set of eigenkets with discrete eigenvalues: $$|P\rangle = \sum^n c_n |p_n\rangle$$ I understand the above. ...
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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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### 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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### 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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### Normalizing 3-Dimensional Wave Function [closed]

How do you normalize a wave function in three dimensions with spherical coordinates?
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If the system if found in the state: $$\psi=\sqrt{\frac{1}{2\pi}}(\frac1{\sqrt3}e^{-i3\phi}+ce^{-i4\phi})$$ what value of $c$ normalizes the wavefunction? Clearly: $$\int_0^{2\pi}\psi^*\psi d\psi=1... 1answer 314 views ### Green's Functions from Gell-Mann and Low Theorem What I want to do: \newcommand{\ket}[1]{\left|#1\right\rangle} \newcommand{\bra}[1]{\left\langle#1\right|} \newcommand{\braket}[1]{\left\langle#1\right\rangle} The Gell-Mann Low Theorem tells ... 3answers 455 views ### Normalization of wave function meaning…? I just have one question. I'm doing a problem where I'm told to normalize a wave function, which is split up into two regions, namely where r \leq r_0 and r > r_0. My question is, why am I ... 1answer 101 views ### How does one normalize this wavefunction? [closed] Here is the question: So I could write  N = \dfrac{1}{{\sqrt{<Ψ|Ψ>}}} , right? Considering the parentheses in the exponential term, it looks like a good idea to switch to spherical polar ... 2answers 4k views ### Why do wave functions need to be normalized? Why aren't the normalized to begin with? [duplicate] Before I started studying quantum mechanics, I thought I knew what normalization was. Just pulling off Google, here's a definition that matches what I've understood normalization to mean: ... 5answers 3k views ### Normalizing the solution to free particle Schrödinger equation I have the one dimensional free particle Schrödinger equation$$i\hbar \frac{\partial}{\partial t} \Psi (x,t) = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} \Psi (x,t), \tag{1}$$with ... 2answers 72 views ### \newcommand{\b}[1]{\langle#1\rangle}Is the expectation of an operator written as \b{\psi|\hat A|\psi} or as \b{\psi|\hat A|\psi}/\b{\psi|\psi}? I had presumed that the expectation of an operator is written as \b{\hat A} = \b{\psi|\hat A|\psi}, but some online reference insists on dividing the entire expression by \b{\psi|\psi}. Since \b{\... 0answers 87 views ### Simplest fermionic normalized quantum many-particle wavefunction in position representation What is the simplest fermionic normalized quantum many-particle wavefunction, expressed in the first-quantized position representation, that you can think of? The normal single-particle examples don't ... 3answers 994 views ### Who is doing the normalization of wave function in the time evolution of wave function? In the Schrodinger equation, at any given time t we should jointly add another sub equation, like$$||\psi_t(x)|| = 1$$where \psi_t(x) = \Psi(x,t), and then try to solve the two equations ... 1answer 953 views ### How do we normalize a delta function position space wave function? [duplicate] I have a position space wavefunction$$\psi(x) = \delta(x-a) + \delta(x+a).$$Now the question states to compute the following: The Fourier transform of \psi(x). (Which invariably is the momentum ... 1answer 61 views ### Normalize Triplet State of Hydrogen For hydrogen, the total spin of the electron and proton is s = 1, while m_s = -1,0,1. If m_s = 1, one of the states can be written as$$\left| 1\;1 \right > = \left |\uparrow \uparrow\right &...
If you are trying to normalize $\psi = A\sin kx$, and you find that $|A|^2 = \frac{2}{a}$, why do you take the positive square root and not the negative? What happens if you take the negative square ...
Let $f(x)$ be a normalised state in a 1-D system. Let $g(x) = iA f(x)$, where $A$ is a Hermitian operator. I want to find the inner product of $g(x)$ with itself. Is it \int \left(-i A^\dagger f^*(...