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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How can quantum wavefunctions be smooth/continuous when particles are created/destroyed/changed?

My (admittedly limited) understanding of the Schrodinger equation tells me that the vector differential operators are only meaningful over a differentiable phase space. For example, if the dimensions ...
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What is the difference between the Bohr model of the atom and Schrödinger's model?

What is the difference between the Bohr model of the atom and The solution of the Schrödinger equation for the hydrogen atom? Are there any difference between definition of the electric potential ...
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Wave packets in Dirac equation

Gaussian wave packets remain Gaussians after evolution in case of the Schrodinger equation. It is a very useful property of these wave packets. I don't think the same is true for a Gaussian wave ...
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Floquet quasienergy spectrum, continuous or discrete?

I haven't got a feeling about Floquet quasienergy, although it is talked by many people these days. Floquet theorem: Consider a Hamiltonian which is time periodic $H(t)=H(t+\tau)$. The ...
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Why does the wavefunction have to be continuous in the presence of a Dirac delta potential?

Considering the time-independent Schrödinger equation, I can see for a finite potential, why the wavefunction has to be continuous, I can also see why the first derivative of the wavefunction is ...
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Quantum Backaction Question

Question about quantum back action in hypothetical scenario: We know that, at $t_0$, a certain kind of particle, with spin initially prepared to be “spin right” in the x basis, goes through a Stern-...
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Probability of measuring an observable $P$ in state $f$, computation [duplicate]

I have state vector $$f(x)=e^{-|x|+ix}$$ and observable $$P=-i\frac {d} {dx}$$ probability that measurement of $P$ in state $f$ will be in $[-1,1]$ I am stuck on this step. I dont know how to take ...
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Energy Expectation Value

I had an assignment question in which I was asked to calculate the expectation value of energy, $\langle E\rangle (t),$ and in the solution to it, the following was stated: \begin{align*} \langle E\...
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Transmission and reflection amplitudes for delta potential Schrodinger equation

I hope this question is not too straightforward for this Q&A site. I have been reading a set of notes in which the transmission and reflection amplitudes for the delta potential Schrodinger ...
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Why is the wave function an element of the function space? [closed]

The general wave function is of the form $$\Psi \left ( x,y,z,t \right )=\psi \left ( x,y,z \right )T\left ( t \right )$$ Solving via separation of variables and finding the product solutions yields,...
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Antisymmetry requirement for the total wavefunction

My understanding is that if we are dealing with a system of two electrons, the total wavefunction needs to be antisymmetric only when the two electrons have same value of n and l ( i.e. they are ...
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What is the Copenhagen interpretation of quantum field theory?

I am most interested in interpretational differences due to the fact that quantum field theory is relativistic while quantum mechanics is not. By "Copenhagen interpretation" I mean a minimal ...
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Measurement of position after collapse of a wavefunction

Suppose I have a wavefunction which collapses to a certain eigenstate after a measurement of energy. In that state, I perform a calculation of position and obtain a certain position value, say $x_0$. ...
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How does wave function collapse when I measure position?

Text books say that when you measure a particle's position, its wave function collapses to one eigenstate, which is a delta function at that location. I'm confused here. A measurement always have ...
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Showing two wavefunctions are proportional to one another [duplicate]

I am struggling to answer the following question: Let ψ₁(x) and ψ₂(x) be normalisable energy eigenfunctions for a particle of mass m in one dimension moving in a potential V(x). Suppose that ψ₁ and ...
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Matter waves and de Broglie wave length

The wavelength of a particle of momentum p is calculated using De Broglie relation. The de Broglie relation was postulated for what is called a matter waves. Now according to the statistical ...
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How do we decide whether an electron orbital has a non-zero or zero probability of lying inside the nucleus of an hydrogen atom?

How do we decide whether an electron orbital has a non-zero or zero probability of lying inside the nucleus of an hydrogen atom? It is mostly from the radial function, as to what I think but how ...
By the Hamiltonian formalism of quantum mechanics, given a quantum system in a state $\Psi$ in a Hilbert space $\mathcal H$, the state will instantaneously evolve in time according to $$\dot{\Psi}=\... 1answer 182 views Continuity behaviour of a wavefunction when the potential exhibits a discontinuity If a potential V(x,t) exhibits a finite discontinuity in space, the wavefunction \phi(x,t) and its spatial derivative will be continuous. If a potential exhibits a finite discontinuity in time, ... 2answers 288 views Time dependent and time independent Schrödinger equations I'm trying to understand the relation between the time dependent and time dependent Schrödinger equations. In particular, we know that the TDSE is$$H\Psi=i\hbar \frac{\partial \Psi}{\partial t}$$... 0answers 53 views solutions of wave equation with cubic term Does the following equation$$ \nabla^\mu \nabla_\mu \psi + a \psi^3 = b \psi $$where \psi is a real function, a and b are real constants, have other solutions that extend beyond a one ... 1answer 100 views Infinite potential well question with wave function \psi (x) = (x -a/2)^2 In an infinite potential well with width a, a particle in this potential well is at state with wave function is \psi (x) = (x -a/2)^2 (not normalized). If you measure the energy of the ... 3answers 93 views Quick way to compute \langle n^{'}l^{'}m^{'}|r^k|nlm \rangle, k \in I; |nlm\rangle is H atom eigenfunction [closed] I want to compute quickly (using maybe some scaling arguments) \langle n^{'}l^{'}m^{'}|r^k|nlm\rangle, where k \in I. |nlm \rangle is the eigenfunction of the Hydrogen atom (H). Example: ... 1answer 85 views Confused on how to interpret the energy eigenfunction of Hydrogen So here is an image of the third lowest energy eigenfunction of an electron in a hydrogen atom: Image from http://imgur.com/Lu4MocL I understand well the eigenfunctions given by Schrodinger's ... 1answer 54 views Spinor expectation value and measurement I have a question about the difference between expectation value and probability of measurement. consider the spinor \zeta = [-3\ \ 4i\ ]^T . The expectation value of S_x is zero because :$$\...
In general quantum mechanics we represent the state of a system with a state vector $| \psi \rangle$ in some Hilbert space in some base. Assuming a complete discrete set of bases vectors \$ |n \rangle ...