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.

learn more… | top users | synonyms

1
vote
0answers
41 views

Continuous spectra and quantum decoherence

Suppose that some quantum wave function $\psi = \int a_i \,i\rangle \,\,di$ where pseudo-spanning ket "vectors" of $\psi$, $i \rangle$, are continuous. (thus the use of integral.) By normalization, $...
2
votes
2answers
150 views

Minimum uncertainity

I'm confused in finding the condition for minimum uncertainty, The author in the book I refer goes on saying that $|g\rangle=c|f\rangle$ is the condition for minimum uncertainity for some constant $...
1
vote
1answer
43 views

Understanding wave functions of matter waves

The wave functions of matter waves give the probability density of the particle being at a certain location. Does this arise because as an outside observer, we have incomplete information about the ...
0
votes
1answer
89 views

Momentum and position for free particle

In the section of 'The free particle' in 'Introduction to quantum mechanics, second edition' by Griffiths page 65. He has the wave equation as $$\Psi(x,t) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{\...
2
votes
2answers
449 views

Probability current vs. direction of wave function

I did an exercise for my Quantum-Mechanics Lecture: Let $\hbar$=2m=1. A particle in 1 dimension has $j(x)=2\ Im(\overline{\psi} (x) \ \psi'(x))$ and it's to show that there are superpositions $\psi (x)...
3
votes
3answers
159 views

Where are the worlds in many-worlds interpretation?

What does it mean in MWI for other universes to exist? Are they in some sector of spacetime beyond our cosmic horizon or is it more complicated? I'm not asking this on Philosophy SE because people ...
0
votes
1answer
194 views

Ground state of a particle in a ring - angular momentum is 0, but it is 'rotating' anyway?

Particle in 1D ring is a textbook problem, but there is one thing I don't understand - if the ground state is considered to have zero angular momentum, then its energy is also zero. And the ...
2
votes
2answers
31 views

Bloch Functions as an implication of the Crystallographic Restriction Theorem?

I'm studying Bloch Functions and it seems to me safe to assume that they are the most general Eigenfunction of a Hamiltionian with the crystal periodicity. Now the only considerations made in deriving ...
1
vote
0answers
91 views

The time evolution in Dirac delta potential [closed]

We know that the dirac delta potential has exactly one bound state. If the potential strength suddenly changes a value, the bound state should evolve to the new bound state, how to describe the time ...
0
votes
3answers
66 views

Is the sum of two stationary states of different energies also a stationary state?

The question title kind of speaks for itself really. I was thinking of maybe using the orthogonality relation to try to show this: $$\int_{-\infty}^{\infty}\phi_n(x)\phi_m(x)dx=\delta_{nm}.$$ ...
1
vote
0answers
65 views

Does an expectation value over only part of a wavefunction have physical meaning?

Does the expression: $$\langle p\rangle_{x=a, b} =\frac{\int_a^b \Psi(x)^*\,\hat{p}\,\Psi(x)dx}{\int_a^b |\Psi(x)|^2dx} $$ have any physical meaning when $\int_a^b |\Psi(x)|^2dx\neq\int_{-\infty}^{\...
4
votes
2answers
339 views

A quantum particle which is almost at rest but whose position is random!

Assume a particle is given by a quantum state which is constructed in such a way that it is equally probable to find it anywhere in an fixed interval $(0,L)$ but has arbitrarily low velocity. The ...
2
votes
5answers
4k views

Complex Conjugate of Wave Function

I've been reading through Griffiths QM book, and the only thing bugging me is they never fully described what $\Psi^* $ should be for any given function. I know it's the complex conjugate at the same ...
3
votes
0answers
61 views

Loss of interference in single-photon Mach–Zehnder interferometer with detector in only one arm

I have read that if you have a Mach–Zehnder interferometer (doing a single-photon experiment) and put a non-destructive detector in only one of the two arms (connected to the first beam splitter), you ...
5
votes
1answer
124 views

Help needed to understand “On the reality of the quantum state”

I am having trouble to understand the reasoning in the following paper, On the reality of the quantum state. MF Pusey, J Barret and T Rudolph. Nature Phys. 8, 475–478 (2012); arXiv:1111.3328. ...
1
vote
1answer
217 views

Single quantum particle in beam splitter, with different systems located in each channel

Suppose a quantum mechanical particle enters a beam-splitter, which sends its wave packets into two mutually orthogonal channels, $C_a$ and $C_b$. Suppose that $C_a$ also contains System A, with ...
0
votes
0answers
28 views

Deriving Wave Function for Scattering States with Delta-Function Potential

I am following the Griffiths Book on Quantum Mechanics, and am following the derivation for the wave function for Delta-Function Potentials. $$V(x) = -\alpha \delta(x)$$ In the scattering states, ...
5
votes
3answers
277 views

How can I solve this quantum mechanical “paradox”?

Let a (free) particle move in $[0,a]$ with cyclic boundary condition $\psi(0)=\psi(a)$. The solution of the Schrödinger-equation can be put in the form of a plane wave. In this state the standard ...
1
vote
1answer
486 views

How to determine the transmission coefficient of a gaussian wave packet scattering on an finite square well?

I am doing a scattering simulation of a Gaussian wave packet on a finite square well. I have solved numerically the Schroedinger equation and I know the values of the wave function after the ...
0
votes
0answers
18 views

Is there a “natural” way to interpolate between a set of bound state wave functions?

Consider for example the Coulomb potential, $-Z/r$, for which there exist a set of bound states with energy $\epsilon_n := {-Z^2 \over 2 n^2}$ (in Hartree). If I want the "wavefunctions" for some ...
1
vote
2answers
256 views

Why does the wave description say that probability oscillates, while the phase interpretation says constant amplitude?

The wave description of a particle illustrates an oscillating probability of the particle being found in any point in space. When a particle travels, it carries along with it a phase that oscillates ...
1
vote
2answers
400 views

Normalized wave functions in position and momentum space

Using the following expression for the Dirac delta function: $$\delta(k-k')=\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(k-k')x}\mathrm{d}x$$ show that if $\Psi(x,t)$ is normalized at time $t=0$, ...
1
vote
1answer
68 views

What's the microscopic and macroscopic effect of wavefunction dispersion?

In Quantum Mechanics (Merzbacher 2nd ed.), problem 2.1 asks us to derive the time evolution of a one-dimensional Gaussian wavefunction (formula given for $t=0$), assuming the velocity is in the $+x$ ...
1
vote
2answers
35 views

Notation of complex valued atomic orbitals

Atomic orbitals are usually labeled $1s$, $2p_x$, $2p_x$, $2p_z$ and so on. These wave functions are defined to be real valued. The original wave functions are complex valued. The $2p_x$ orbital is ...
1
vote
0answers
58 views

Expectation value of the Hamiltonian [closed]

How to calculate expectation value of the Hamiltonian for hydrogen atom? $$\langle H \rangle_{\alpha l} \equiv \frac{\langle \psi_{\alpha l m}|H(r)| \psi_{\alpha l m}\rangle} {\langle \psi_{\alpha l ...
0
votes
0answers
43 views

How to rewrite a wave function in terms of spheical harmonics

I'm given a wave function for a particle, in three variables (spherical coordinates): $ψ=ψ(r, θ, φ) = re^{-r/a}sin(θ)sin(φ)$. I'm tasked with rewriting $ψ$ in terms of spherical harmonics which are ...
0
votes
1answer
64 views

Energy of hydrogen atom - Schrodinger equation [closed]

The wavefunction of the electron in the hydrogen atom is $ k* exp(-r/a)$ (k is the normalization constant), but it does not take n into account, whereas the solution of Schrödinger's equation ($H(...
0
votes
1answer
91 views

Clarification about two forms of the wave function

The wave function in the position representation is $\langle\ x\rvert\psi\rangle$ = $ \psi (x) $ , where $ \psi (x) $ are the continuous coefficients that multiply the orthonormal basis vectors, i.e, $...
0
votes
2answers
3k views

Periodic boundary condition on a Wave Function of a Particle in a Box

Until now, solving the Schrodinger Equation for a particle in a box was relatively easy because the boundaries conditions imposed zero value on the wave function at the boundaries. But now I must find ...
0
votes
2answers
97 views

Difference for boundary condition, particle in a box

When solving the simple problem of a free particle in a box of volume $V = L^3$, we can impose either periodic boundary conditions $\psi(0) = \psi(L)$ and $\psi '(0)= \psi'(L)$ either strict boundary ...
2
votes
2answers
234 views

Hartle and Hawking's universal wavefunction

My apologies in advance if this question is poorly worded or doesn't make any sense, however I have just finished reading into this theory and it seems as though Hawkings No Boundary Universe is ...
2
votes
1answer
96 views

How to calculate the frequency of oscillation of superposition states [closed]

Been working on this question for a while and I'm not sure how to go about it. Could someone point me in the right direction, particularly for the frequency question. The question is as follows: A ...
5
votes
4answers
857 views

How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics?

$$\langle x^2 \rangle = \int_{-\infty}^\infty x^2 |\psi(x)|^2 \text d x$$ What is the meaning of $|\psi(x)|^2$? Does that just mean one has to multiply the wave function with itself?
1
vote
1answer
44 views

Why wavefunction is sometimes multiplied by the radius to get probability density?

When solving 1d particle in a box, the probability density is said to be proportional to $|\psi|$, but when solving 3d orbitals, the probability density is said to be proportional to $|\psi|^2 r^2$. ...
0
votes
1answer
59 views

Two fermions with total spin 1 antisymmetric wave function? [closed]

How can I prove, that two fermions with a total spin of 1 must have an antisymmetric wave function?
1
vote
1answer
55 views

Can we measure the energy of one of several identical particles?

Suppose we have a many-particle system described via a many-particle wavefunction that involves single-particle states $\lvert\lambda_{a}\rangle$, $\lvert\lambda_{b}\rangle$, $\lvert\lambda_{c}\rangle$...
0
votes
3answers
187 views

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 ...
3
votes
2answers
27k views

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 ...
1
vote
0answers
46 views

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 ...
6
votes
2answers
488 views

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 ...
0
votes
1answer
99 views

Derivation of group velocity using Fourier transform

The aim is to determine the group velocity of a wave packet with the general form $$\Psi\left(x,t\right)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} \phi\left(x\right)e^{i\left(kx-\omega t\right)}dk....
0
votes
0answers
25 views

Why can a free particle not exists in a stationary state? [duplicate]

In normalising the complete wavefunction of a free partcile; $V(x)=0$ we arrive at $\int_{-\infty}^{\infty}\Psi_{k} ^\dagger\Psi_{k}dx=|A|^{2}\int_{-\infty}^{\infty}dx=|A|^{2}\left(\infty\right)$ ...
0
votes
0answers
51 views

How can we fix the constant of the energy eigenstates of a quantum free particle such that they satisfy the orthonormality condition?

For a quantum free particle, the momentum and energy eigenstates are compatible. The constants of the momentum eigenstates are fixed by their orthonormality. Similarly, how can we fix the constant for ...
0
votes
0answers
21 views

For a quantum free particle, would it be possible to relate the wavefunction $a_E(E)$ in energy basis and $a_p(p)$ in momentum basis?

The energy for a free particle has continuous energy eigenvalues $E$. Let $u(E,x)$ be its energy eigenstates in position basis. Its wavefunction $\psi(x,t)$ can be expressed as \begin{align} \psi(x,t)...
1
vote
1answer
97 views

Tricky particle in an infinite potential well question

For a particle in an infinite square-well potential in an energy eigenstate, the probability distribution relating to outcomes of position measurements vanishes outside the square well and takes a ...
3
votes
0answers
52 views

In quantum descriptions of atoms why are observables (which we derive from the wave function) attributed to electrons?

For example the orbital angular momentum, for the hydrogen atom. Is this the total angular momentum of the atom(electron and proton) or just the electron? I am asking because, I am learning about how ...
-1
votes
3answers
88 views
-1
votes
4answers
297 views

Why does the electron wave function collapse in a double slit experiment?

Did the electron wave function collapse in the double slit experiment due to being observed, OR is it that the electron wave function collapsed because the instrument used to measure it physically ...
1
vote
1answer
78 views

Physical interpretation of the constant coefficient appearing in solution to the Schrodinger equation

The product solution to the Schrodinger's equation is $$\Psi_{n} \left ( x,t \right )=\psi\left ( x \right )\phi\left ( t \right )$$ By superposition, the solution becomes $$\Psi \left ( x,t \...
3
votes
2answers
229 views

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 ...