# Questions tagged [wavefunction]

A complex scalar field that describes a quantum mechanical system. The square of the modulus of the wave function gives the probability of the system to be found in a particular state. DO NOT USE THIS TAG for classical waves.

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### How do I use first-order perturbation theory to compute the first four energy levels related to a potential well?

I came across a problem whose statement is as follows: An electron moves in the potential well $P (x) = -\delta$ for $- a <x <0$ and $P (x) = \delta$ for $0 <x <a$ (Fig. 13.7). Use first-...
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### Entanglement networks and perspective

So, superposition/entanglement is supposed to be fragile because, if any information leaks from the system, the wave function collapses. However, the very definition of 'information leaking' must set ...
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### Unanswered Question on Potential Step Function

I have looked at the questions on this stack exchange and did not find a single convincing answer. Please absolutely remember the mathematical definition of only 4 things as you read this. Probability ...
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### Measuring momentum

I'm new here, possibly my apologies for misplacing. After a measurement in quantum mechanics, the wavefunction collapses to an eigenstate corresponding to the outcome of the measurement. Thus if we ...
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### Can we handle the wave function as if it was a real valued function? [duplicate]

I am trying to analyze in general simple one dimensional QM problems. To be more specific let's consider this kind of Hamiltonian: $$H=\frac{\hat{p}^2}{2m}+V(\hat{x})$$ From this one we can derive the ...
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### Mirror/Parity symmetry

I am trying to solve a problem of Griffiths' book. $\hat{\Pi} \psi(\vec{r}) = \psi(-\vec{r})$ where $\vec{r}$= (x,y,z), eq. (1) $\hat{\Pi}$ is the parity operator. The problem says to show that ...
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### Average over the Bloch sphere

Consider you have a function of a two-level wave quantum state $f(\vert \psi \rangle )$, with $\vert \psi \rangle = \alpha \vert 0 \rangle + \beta e^{\rm i \phi} \vert 1 \rangle$. With no loss of ...
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### What will happen if I multiply a ket vector by a complex number?

I was reading Zettili’s Quantum Mechanics book. There I have seen when a ket (or bra) multiplied by complex number, we also get a ket (or bra) But how do we infer this by mathematics?
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### Complex Nature of the Wavefunction

I am doing this problem and I realized the wavefunction is real. But we also already showed that the wavefunction needs to be complex. Why is it that the wavefunction given here is real? I first ...
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### Transition between 2 energy levels - wave function picture

Suppose we have a system that has discrete energy levels (e.g. hydrogen atom, potential well) and the stationary solutions for the wave function are $\psi_n$. I would assume that there should be a way ...
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### 'Deriving' superposition representations for 3 particles

I'm trying to write up all the possible superposition states for 3 spin-1/2 particles (one spin-up, 2 spin-down). Lets denote $|\uparrow \rangle = |0\rangle, |\downarrow \rangle = |1\rangle$. ...
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### Do quantum wave functions rotate through imaginary space?

Watching a visualization of Schrödinger’s equation, I noticed that the wave function for a 2-dimensional particle was placed in a 3-dimensional graph consisting of 2 Real axes and an Imaginary axis. ...
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### Is the wave packet of a relativistic quantum particle oblate (flattened) or prolate (elongated)?

A free, non-relativistic wave packet of a quantum particle is usually thought of as having spherical shape. What happens for a particle moving relativistically? For an outside observer, is the wave ...
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### Question on Probability Amplitudes

The Born rule implies that the probability density $\rho$ is defined as $$\rho(x,y,z)=|\psi(x,y,z,t_0)|^2$$ at time $t_0$. What is the difference in this probability density and the probability of a ...
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### Finite double potential barrier transmission coefficient

TL;DR: I want to calculate the transmission coefficient of a particle travelling into a finite double potential barrier system and I think I've got stuck by the fact that I have 9 unknown variables (...
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### Question about an “empty ket” and Dirac's notation

This question is related to this other one and it's about Bra-Kets formalism. Hope I'm not bothering you but the truth is I'm very confused. Reading 1939 Dirac's publication on Bra-kets notation "...
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