Tagged Questions

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.

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Expectation value of an Observable and Eigenstates

I am learning about Quantum Mechanics at the moment and I was wondering about Eigenfunctions and Observables. The question I would like to ask is, If a wavefunction is not an eigenstate of an ...
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How to plot numerically the wave functions according to the Hamiltonian?

It is often difficult to analytically solve the Schrodinger equation, and so we need to obtain a solution numerically. An example plot is shown below. Here, the wave functions for a three junction ...
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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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44 views

Rotating fermion and spin structure on manifold

We know that doing a 2$\pi$ rotation would give a minus sign to wavefunctions of electrons. Since electrons are spin $1/2$ objects. How is this related to the spin structure on the manifold in which ...
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23 views

Conditions to find standing waves harmonics

I came up with a doubt on standing waves conditions. The type of question I find difficult to answer is of the following type. Consider a rope. I do not know if the rope is fixed at both end or at ...
1answer
32 views

Situations in which there is path difference interference or formation of standing waves [on hold]

I came up with a doubt about standing waves and path difference in general. Consider these two different cases as examples. If I have a rope fixed at one end and I make the free end oscillating, I ...
3answers
554 views

Quantum Mechanics in Electric Field

I am working on a problem which looks like this. Consider a charged particle with charge $q$ trapped in a box of length $L$ with finite constant potential $V_0$ on both ends. A constant (static) ...
4answers
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What does the Schrodinger Equation really mean?

I understand that the Schrodinger equation is actually a principle that cannot be proven. But can someone give a plausible foundation for it and give it some physical meaning/interpretation. I guess I'...
2answers
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General formula for expanding wave function in terms of orthogonal states?

Given a wave function $\psi(x) = \langle \psi | x \rangle$. It can be expanded in terms of orthogonal states: $$\langle \psi | x \rangle = \sum_n \langle \psi | n \rangle \langle n |x \rangle$$ ...
1answer
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How to understand permutations of particles in Quantum Mechanics?

I'm studying identical particles in Quantum Mechanics and I'm having a hard time to understand the idea of permutations of particles from a mathematical standpoint. From one intuitive point of view ...
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Why does a electric Potential have to be real, but not a Potential in quantum mechanics?

So I had this Problem when I had to learn about classical electromagnetism: Why is it, that we use complex numbers when calculating stuff, but in the end only the real part is important (for example ...
3answers
2k views

When Eigenfunctions/Wavefunctions are real?

When the Hamiltonian is Hermitian(i,e. beyond the effective mass approximation), generally under which conditions the eigenfunctions/wavefunctions are real? What happens in 1D case like the finite ...
5answers
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What happens when two wavefunctions meet?

Apologies for the over-broad question(s), but I'm having a hard time finding out where to look to answer these myself: If a particle is a wavefunction describing a probability amplitude distributed ...
1answer
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Can a quantum mechanical system have more than one wave-function?

I was told that a quantum mechanical system is completely determined by its wave function. But superposition principle says that given two wave functions of some system, a linear combination of them ...
1answer
38 views

Protocol for solving time independent Schrodinger equation

Just a short question about the protocol for solving the time-independent Schrodinger equation for different potentials and the reasons for accepting and rejecting solutions. Take for example the ...
3answers
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Can a physical wavefunction be non-smooth (its first derivative is discontinuous)?

Here's an argument that might support the statement that such a non-smooth wavefunction is not physical: You cannot add a finite number of smooth functions to get a non-smooth function. By fourier ...
1answer
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Modern interpretation of wave-particle duality

As far as I understand, in the early days of quantum theory there was quite a lot of debate over how to interpret what it meant for a quantum mechanical object to exhibit both wave-like and particle-...
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Energy Conservation in Changing Potential Well

If you prepare a particle in a basis state, $|n\rangle$ of an infinite potential well of length $L$, the energy of that state will be $\langle E\rangle = E_n$, with zero variance. If you then ...
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What is so special about atomic nodes and why do they exist? [duplicate]

Using Schrodinger’s wave equation we see that there are certain nodes, i.e radial nodes where the probability of finding the electron is minimum. These nodes are sometimes very close to the nucleus ...
1answer
204 views

Probability and double slit

if a beam of identical particles at random distances from each other (or exactly 1/2 lambda between each other) travelling with the same v towards a double sllit do not interfere with each others wave ...
2answers
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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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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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Where does the position operator come from?

In quantum mechanics the momentum and energy operators appear in Schroedinger's equation. In fact in the derivation of Schroedinger's equation from the classical wave equation the momentum operator ...
1answer
54 views

Finding the velocity of a given wavepacket [closed]

I've been given a wave packet, that is moving from right to left toward a (known) potential, which has in time $t = 0$ has the form: $$ψ(x, t = 0) = Ae^{−c(x−x_0)^2}e^{ik_0x}$$ and I need to ...
2answers
223 views

Can we write the wave function of the living things? If yes then how? [closed]

In quantum mechanics we studied that everything has a wave function associated with it.My question is can we write down the wave functions of things. Then how we can write down the wave functions of ...
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Can Schrödinger Equation be derived from Huygens' Principle?

Notes of Enrico Fermi start from an analogy between mechanics and optics and with 4 pages he derives the Schrödinger equation. In all my courses, I have seen as an axiom - this is how wave-particles ...
1answer
64 views

Can particle quantum spin be described with a wave function? [closed]

I'm a little confused about the idea of spin. It's been non-technically described to me as "like magnetic dipole moment", except only two possible "directions". But I feel like that's a bad analogy, ...
0answers
20 views

Can someone explain what the wave function is? [duplicate]

I've been doing she research I don't really understand what a wave function is. I used to think it was the de Broglie's wavelength but I've soon found otherwise. Just a simple and clear explanation ...
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Wavefunctions “adapted” to the perturbation ? Relation to Faraday effect

I came accross the following statement in a book: If one wants to switch on a magnetic field, one must first choose the appropriate complex unperturbed wave functions (that are "adapted" to the ...
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Wavefunction of electron in 3D infinite well with non-zero potential

Consider an electron moving in a potential $V$ defined by $$V(x,y,z) = \left \{ \begin{array}{ll} \alpha(x^2 + y^2) & 0 \leq z \leq a \\ \infty & \text{otherwise} \end{array} \right.$$ ...
2answers
823 views