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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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 ...
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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 ...
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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 ...
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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 ...
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2answers
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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:
...
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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 ...
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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} \...
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1answer
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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.
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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 ...
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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 $...
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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 ...
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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 ...
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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 ...
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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)$...
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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$$
Note that here $|\psi\rangle$ ...
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23 views
Wavefunction and associated energies of particle in uniform magnetic field [closed]
I'm trying to find the wavefunction and associated energies of a charged particle in a uniform magnetic field .
We have the following hamiltonian:
$$ H = \frac{(-i\hbar\nabla -q\vec{A})^2}{2m} $$
...
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1answer
84 views
Instantaneous quantum features
Two of the most striking quantum oddities are entanglement and the wave-function collapse or state vector reduction.
Firstly, quantum entanglement is the quantum phenomena involving states of ...
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1answer
48 views
Density overlap of orthogonal wavefunctions
Intuitively, I suspect that orthogonal wavefunctions don't have much overlap in their densities. For example, in separable approximations of many-body fermions like Hartree-Fock, the wavefunctions of ...
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2answers
213 views
Normalization constant of a planar wave
As we know for the plane waves ( $ae^{i k x}+b e^{-i k x}$), the normalization constant can be easily obtained from the integral $\int^{x_{2}}_{x_{1}}\psi^{*}\psi dx=1$ by the relation $|a|^{2}+|b|^{2}...
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1answer
105 views
Is width of particles a consequence of Heisenberg's uncertainty principle?
The uncertainty principle tells us that
$$\sigma_x\sigma_p \geq \frac{\hbar}{2}, $$
which means that the more precisely we measure a particle's position, the more imprecise we will know its momentum. ...
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1answer
26 views
How do you apply the antisymmetrization operator?
I have an expression like,
$Y^{L M_L}_{l_1 l_2}(\Omega_1, \Omega_2) = \sum_{m_1 m_2} \langle l_1 m_1l_2m_2|L m_L\rangle Y_{l_1m_1}(\Omega_1) Y_{l_2m_2}(\Omega_2)$ ,
as the angular part of a two ...
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1answer
31 views
Bound states and parity for a arbitrary potentials
If we are given an arbitrary potential, and we are asked to find bound states and parity, what would be usual strategy to do that?
Let's we have a potential given:
$$-\frac{A}{y^2+a^2} -\frac{A}{(y-...
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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 ...
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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
$$\Psi^*\...
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34 views
Wave packet - phase vs group velocity
So, I've been revising QM recently and the concept of group vs phase velocity has me confused.
Let's say we have a wave packet. As quoted in Griffiths, "...A wave packet is a superposition of ...
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1answer
101 views
Can wavefunctions be real? [closed]
I remember proving that real wavefunctions have zero expectation value for momentum and don't define any useful physical states. But still for a particle in infinite potential well the wavefunction is ...
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1answer
59 views
How to determine initial quantum state? [closed]
A particle in an infinite square well has its initial wave function an
even mixture of the first two stationary states:
$$\psi(x,0)=A(\psi_1(x)+\psi_2(x)) $$
As you may know, for $\psi(x,t)$ we ...
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0answers
54 views
Issue with solving for the wavefunction of a simple infinite potential
For the potential given by $V(x)=\left\{\begin{array}{ll}{\infty} & {x<0} \\ {-V_{0}} & {0<x<a} \\ {0} & {a<x}\end{array}\right.$
I am trying to solve for the wavefunction. ...
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33 views
I need to find the probability of measuring certain energies with the given linear combination wavefunction
I have a group of wavefunctions given by $\psi_{n}(x)=\left\{\begin{array}{ll}{\sqrt{2 / a} \sin (n \pi x / a),} & {0 \leq x \leq a} \\ {0,} & {\text { otherwise }}\end{array}\right.$
I also ...
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1answer
62 views
Why don't expectation values for a stationary state evolve over time?
I have an observable $O$ with operator $\hat{O}$. $\Psi_1$ is a wave function in an energy eigenstate, and $\psi_1$ is the corresponding spatial wave function. $E$ is the corresponding energy.
It is ...
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2answers
39 views
The link between discrete energy level in quantum mechanics and harmonic series in Acoustics
Consider a quantum square potential well with infinite depth:
$$
V(x)=\begin{cases}
0, &|x|<a \\
+\infty, &\text{otherwise}.
\end{cases}$$
Solving the Schodinger equation of a particle with ...
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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
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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 ...
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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?
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1answer
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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 ...
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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, ...
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3answers
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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, & \...
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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 ...
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1answer
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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 ...
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2answers
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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 $P_n = \int_{-\...
3
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2answers
155 views
If the wavefunction is continuous how can the many-worlds be discrete?
Preamble for clarity:
The many worlds interpretation is usually used to explain the measurement of a 2 level system ($|0\rangle$ or $|1\rangle$) as:
$$\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)|\text{...
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2answers
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Integral as summation in quantum mechanics
I have just started QM and one thing that keeps bugging me is that whenever we have a continuous summation we take it as an integral (like in the formula below)... So why can we do this why summation ...
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2answers
91 views
What is probability amplitude and why is it complex?
When dealing with Mach-Zender interferometers the professor usually lets $\alpha$ & $\beta$ denote the probability amplitude that a particular photon isn't reflected by the beam splitter and the ...
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2answers
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What is difference in Dirac Notation for probability and Probability Density in Quantum Mechanics? [closed]
The Dirac Notation for wave function
$$\langle\psi|\psi\rangle= \int_{-\infty}^\infty \psi^{*}\psi \,dx $$
$$\text{Probability} = \int_{-\infty}^\infty \psi^{*}\psi \,dx $$
But most often it is ...
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2answers
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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 ...
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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 ...
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Stationary State of Quantum Mechanics [duplicate]
Why for every normalized solution to the time-independent Schrödinger equation $E$ must exceed the minimum value of $V(x)$?
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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 ...
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2answers
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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 ...
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1answer
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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 ...
