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.

Filter by
Sorted by
Tagged with
-1
votes
0answers
19 views

Normalization of Airy function [on hold]

I hv to normalize this wave functiom but due to airy function,I hv no idea how to normalize this.I also check the landau and lifshitz.vol.3.Quantum mechanics non relativistic theory,pg#74, I didn't ...
1
vote
2answers
59 views

How can this represent the wave function?

How can $\psi=Ae^{i(kx-\omega t +\phi)}$ represent a plane wave travelling in $+x$ direction? I knew the equation $\psi = A\cos(kx - \omega t + \phi)$. I also know Euler's identity and that the ...
0
votes
1answer
55 views

Finite-time Fourier transform of a wavefunction

Can someone explain this formula to me? Given a wave packet whose time evolution is $g(t)$, a partially resolved spectrum is found by Fourier transforming its overlap with the same wave packet at ...
0
votes
1answer
21 views

Quantum Interference Pattern with Perpendicular Sources

Imagine that there is a photon detector in front of me. Also imagine that there is a test photon traveling from my left to my right. As this test photon passes, I fire other photons right at the ...
3
votes
2answers
52 views

Sequential Double Double Slit Experiment?

Let's say you arrange the double slit experiment so that there are two sets of two slits one after the other. Like so: ...
0
votes
0answers
32 views

Are stationary states always real functions? [duplicate]

I've noticed that for many quantum potentials, (the harmonic oscillator, the infinite square well, and the delta potential) the wavefunctions $\psi_n$ of stationary states are always real valued ...
1
vote
1answer
50 views

Proof that momentum operator acting on a wavefunction gives the expectation value

I'm following a book where the author tries to prove that $$\langle p \rangle = \langle \psi \vert \hat{p} \vert \psi \rangle,\tag{0}$$ so he just computes the integral $$ \langle \psi \vert \hat{p} \...
-2
votes
1answer
56 views

Why can't the wave function and it's derivative be zero at the same point? [duplicate]

This was discussed before proving the node theorem.
10
votes
5answers
1k views

Which basis does the wavefunction collapse to?

When we measure position for example, how does the system "know" that we're measuring position in order to collapse to a position eigenvector? Does the wave function always evolve from the state that ...
0
votes
1answer
110 views

Which wave function should I adopt?

Suppose I have Hamiltonian $H_0(\hat{p},\hat{r})$, it satisfies $H_0\psi(p,r)=E(p)\psi(p,r)$. If I make a change from $\hat{p}\to\hat{p}+p_0$, what is the form of the wave function of the Hamiltonian $...
0
votes
1answer
103 views

A Schrödinger Love Poem? [on hold]

This question is for those who can see the romantic side of the Schrödinger equations... My GF is studying quantum mechanics, and I was thinking to write it as an expression of a two-particle ...
1
vote
0answers
41 views

Wavefunction of particle in power law potential of type $x^a$?

How could we calculate the wave function of a particle under a potential of form $V(x)=x^a$? Is there any analytical solution or any general feature of such solution (like its an exponential ...
0
votes
0answers
24 views

How is it possible to build such large interferometers?

How is it possible to build interferometers of virtually any width when the tiny photon wave packets entering each side of them, which are then made to interfere with themselves, would seem to need to ...
0
votes
1answer
55 views

${}$ Dirac delta potential

We know that the number of bound states for an attractive delta potential is one. If so what will the number of bound states for a particle in a repulsive delta potential? If $V(x)= +a \cdot \delta(x)$...
1
vote
1answer
71 views

What is $\frac{d}{d\psi}\langle\psi| \hat{O} | \psi\rangle$?

I would like to know what is the derivative of an expectation value with respect to the molecular state $$\frac{d}{d\psi}\langle\psi| \hat{\mathbf{O}} | \psi\rangle$$ Note that here $|\psi\rangle$ ...
0
votes
0answers
23 views

Wavefunction and associated energies of particle in uniform magnetic field [closed]

I'm trying to find the wavefunction and associated energies of a charged particle in a uniform magnetic field . We have the following hamiltonian: $$ H = \frac{(-i\hbar\nabla -q\vec{A})^2}{2m} $$ ...
0
votes
1answer
84 views

Instantaneous quantum features

Two of the most striking quantum oddities are entanglement and the wave-function collapse or state vector reduction. Firstly, quantum entanglement is the quantum phenomena involving states of ...
1
vote
1answer
48 views

Density overlap of orthogonal wavefunctions

Intuitively, I suspect that orthogonal wavefunctions don't have much overlap in their densities. For example, in separable approximations of many-body fermions like Hartree-Fock, the wavefunctions of ...
3
votes
2answers
213 views

Normalization constant of a planar wave

As we know for the plane waves ( $ae^{i k x}+b e^{-i k x}$), the normalization constant can be easily obtained from the integral $\int^{x_{2}}_{x_{1}}\psi^{*}\psi dx=1$ by the relation $|a|^{2}+|b|^{2}...
4
votes
1answer
105 views

Is width of particles a consequence of Heisenberg's uncertainty principle?

The uncertainty principle tells us that $$\sigma_x\sigma_p \geq \frac{\hbar}{2}, $$ which means that the more precisely we measure a particle's position, the more imprecise we will know its momentum. ...
0
votes
1answer
26 views

How do you apply the antisymmetrization operator?

I have an expression like, $Y^{L M_L}_{l_1 l_2}(\Omega_1, \Omega_2) = \sum_{m_1 m_2} \langle l_1 m_1l_2m_2|L m_L\rangle Y_{l_1m_1}(\Omega_1) Y_{l_2m_2}(\Omega_2)$ , as the angular part of a two ...
0
votes
1answer
31 views

Bound states and parity for a arbitrary potentials

If we are given an arbitrary potential, and we are asked to find bound states and parity, what would be usual strategy to do that? Let's we have a potential given: $$-\frac{A}{y^2+a^2} -\frac{A}{(y-...
9
votes
1answer
156 views

How is the quantum propagator related with Huygens principle?

Usually in quantum mechanics the wave function can be propagated via the so-called Kernel or Amplitude: $\Psi(x,t) = \int K(x,t;x',t')\Psi(x',t')dx'$. I have read in some paper that this comes from ...
0
votes
0answers
49 views

Wavefunction of a self-adjoint operator

A self adjoint operator in general can be written as $$\mathscr{L(x)}=\frac{d}{dx}\big[ p_0(x)\frac{d}{dx}\big]+p_2(x)$$ The probability current associated can be found in the standard way $$\Psi^*\...
1
vote
0answers
34 views

Wave packet - phase vs group velocity

So, I've been revising QM recently and the concept of group vs phase velocity has me confused. Let's say we have a wave packet. As quoted in Griffiths, "...A wave packet is a superposition of ...
0
votes
1answer
101 views

Can wavefunctions be real? [closed]

I remember proving that real wavefunctions have zero expectation value for momentum and don't define any useful physical states. But still for a particle in infinite potential well the wavefunction is ...
-1
votes
1answer
59 views

How to determine initial quantum state? [closed]

A particle in an infinite square well has its initial wave function an even mixture of the first two stationary states: $$\psi(x,0)=A(\psi_1(x)+\psi_2(x)) $$ As you may know, for $\psi(x,t)$ we ...
1
vote
0answers
54 views

Issue with solving for the wavefunction of a simple infinite potential

For the potential given by $V(x)=\left\{\begin{array}{ll}{\infty} & {x<0} \\ {-V_{0}} & {0<x<a} \\ {0} & {a<x}\end{array}\right.$ I am trying to solve for the wavefunction. ...
1
vote
0answers
33 views

I need to find the probability of measuring certain energies with the given linear combination wavefunction

I have a group of wavefunctions given by $\psi_{n}(x)=\left\{\begin{array}{ll}{\sqrt{2 / a} \sin (n \pi x / a),} & {0 \leq x \leq a} \\ {0,} & {\text { otherwise }}\end{array}\right.$ I also ...
1
vote
1answer
62 views

Why don't expectation values for a stationary state evolve over time?

I have an observable $O$ with operator $\hat{O}$. $\Psi_1$ is a wave function in an energy eigenstate, and $\psi_1$ is the corresponding spatial wave function. $E$ is the corresponding energy. It is ...
2
votes
2answers
39 views

The link between discrete energy level in quantum mechanics and harmonic series in Acoustics

Consider a quantum square potential well with infinite depth: $$ V(x)=\begin{cases} 0, &|x|<a \\ +\infty, &\text{otherwise}. \end{cases}$$ Solving the Schodinger equation of a particle with ...
-2
votes
1answer
42 views

Does entropy increase in an isolated quantum system undergouing unitary evolution?

Does the second law of thermodynamics still work without wavefunction collapse? I received these contradicting answers on Quora: https://qr.ae/TWvoOC https://qr.ae/TWvoO4
2
votes
2answers
73 views

QM probability density function without Born's rule, invariant to wave-function phase

The QM probability density as a function of the wave function is given by Born's rule as a postulate. This leads to the probability density being invariant to the phase of the wave function. Suppose ...
0
votes
1answer
61 views

Solutions that are part of the Hilbert space

Why do we omit solutions that do not converge at $\pm\infty$ from the physical Hilbert space, what is the argument for us being allowed to do so?
2
votes
1answer
79 views

Question about the “wave function” on Relativistic Quantum Mechanics (RQM) and Quantum Field Theory (QFT)

I'm enrolled on a short and conceptual couse on RQM and QFT and the professor made a distinction about the Klein-Gordon (K-G) equation on RQM and the K-G equation on QFT. Roughly speaking, he said ...
1
vote
2answers
69 views

Why doesn't the amplitude of a wave-function fall off to zero immediately at a potential barrier?

When a wave function in QM potential well problems interact with a potential barrier with height more than the energy of the wave, the amplitude of the wave doesn't immediately falls off to zero, ...
1
vote
3answers
77 views

Negative energy in bound states of a particle in a finite potential well

Consider you have a particle in a finite potential well as depicted in the photo attached. Now we have three regions: $$V(x) = \begin{cases} 0, & \text{for } x<-a & (1)\\ -V_0, & \...
0
votes
0answers
57 views

Quantum mechanics states

An electronic state is defined by Ψ(θ,φ) means it is dependent on θ and φ, but after repeated measurements it is found that electron's position is independent of Θ and φ. What is its physical and ...
0
votes
1answer
31 views

The overlap of two Slater determinant states

Suppose I have two fermionic number states in different bases, with the same particle number $N$ - call them $|\Psi\rangle$ and $|\Phi\rangle$. In the position basis, I can write the many-body ...
0
votes
2answers
83 views

Calculate the $n^{th}$ energy state given the wavefunction?

I am given the wavefunction $\psi(x,t)$. How does one determine the probability of a measurement of the energy giving the $n^{th}$ eigenstate? My guess is it should be something like $P_n = \int_{-\...
3
votes
2answers
155 views

If the wavefunction is continuous how can the many-worlds be discrete?

Preamble for clarity: The many worlds interpretation is usually used to explain the measurement of a 2 level system ($|0\rangle$ or $|1\rangle$) as: $$\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)|\text{...
1
vote
2answers
99 views

Integral as summation in quantum mechanics

I have just started QM and one thing that keeps bugging me is that whenever we have a continuous summation we take it as an integral (like in the formula below)... So why can we do this why summation ...
3
votes
2answers
91 views

What is probability amplitude and why is it complex?

When dealing with Mach-Zender interferometers the professor usually lets $\alpha$ & $\beta$ denote the probability amplitude that a particular photon isn't reflected by the beam splitter and the ...
0
votes
2answers
84 views

What is difference in Dirac Notation for probability and Probability Density in Quantum Mechanics? [closed]

The Dirac Notation for wave function $$\langle\psi|\psi\rangle= \int_{-\infty}^\infty \psi^{*}\psi \,dx $$ $$\text{Probability} = \int_{-\infty}^\infty \psi^{*}\psi \,dx $$ But most often it is ...
0
votes
2answers
51 views

Can the wave-function of any particle in any basis be written as a matrix?

Can the wave-function of any particle in any basis be written as a matrix? If no, how can we explain this, where the Hamiltonian $H$ in U is a QM operator that can be written as a linear ...
0
votes
1answer
39 views

Schrodinger equation: If $V(x)=V(-x)$ then prove that $\psi(x)=\psi(-x) $ or $\psi(x)=-\psi(-x)$ [duplicate]

The title explains itself. If the potential is an even function then prove that wave function is either odd or even. I set $-x$ in Schrodinger equation and find out that $\psi(-x)$ is also a solution ...
0
votes
0answers
35 views

Stationary State of Quantum Mechanics [duplicate]

Why for every normalized solution to the time-independent Schrödinger equation $E$ must exceed the minimum value of $V(x)$?
2
votes
1answer
100 views

Momentum Wave Function gives strange expectation values

Suppose there's a particle with the wave function $\psi(x)=\frac{1}{\sqrt{L}}$ for $0<x <L$ and 0 everywhere else. One way to get the associated Momentum Wave function is direct integration on ...
-3
votes
2answers
50 views

Understanding wave function graph

I found this graph from the internet that interprets the graphical representation of wave function.I completely understand the wave function that is depicted by blue line but i really am confused ...
1
vote
1answer
67 views

Understanding the quantum mechanical state vector

According to Griffiths, there is a general state vector $|s(t)\rangle$ that encodes the state of the system. He also says that we take $\Psi(x, \ t) \ = \ \langle x | s(t) \rangle$. Would then mean ...