For the sake of this question, I am primarily concerned with the position wave function. So, from my understanding, the wave function seems to 'collapse' to a few states apon measurement. We know this because, if the same particle is measured again shortly after this, it will generally remain in...
May i know how do i eliminate C and D and how do i obtain the last two equations? Are there skipping of steps in between 4th to 5th equation? What are the intermediate steps that i should take to transit from 4th equation to the 5th equation?
I've been reading about Quantum Field Theory and what it says about subatomic particles. I've read that QFT regards particles as excited states of underlying quantum fields.
If this is the case, how can particles be regarded as objective? It seems to me that this also removes some of the...
Hi everyone!
This is the first time I'm posting on any forum and I'm still rather unsure of how to format so I'm sorry if it seems wonky. I'll try my best to keep the important stuff consistent!
I am working on infinite square well problems, and in the example problem:
V(x) = 0 if: 0 ≤ x ≤ a...
Elementary question: Is there ever a case where the solutions for a wave equation turn out not to be a vector (in Hilbert space of infinite complex-valued dimensions, or a restriction to a subspace thereof) , but something else -- say, (higher-order) tensors or bivectors, or some such?
My...
As we see in this Phet simulator, this is only the real part of the wave function, the frequency decreases with the potential, so lose energy as moves away the center.
we se this real-imaginary animation in Wikipedia, wave C,D,E,F. Because with less energy, the frequency of quantum wave...
Hello!
I am stuck at the following question:
Show that the wave function is an eigenfunction of the Hamiltonian if the two electrons do not interact, where the Hamiltonian is given as;
the wave function and given as;
and the energy and Born radius are given as:
and I used this for ∇...
The book on quantum mechanics that I was reading says:
d<x>/dt = d/dt ∫∞-∞ |ψ(x,t)|2 dx
=iħ/2m ∫∞-∞ x∂/∂x [ψ∂ψ*/∂x+ψ*∂ψ/∂x]dx (1)
=-∫∞-∞ [ψ∂ψ*/∂x+ψ*∂ψ/∂x]dx (2)
I want to know how to get from (1) to (2)
The book says you use integration by part:
∫abfdg/dx dx = [fg]ab - ∫abdf/df dg dx
I chose f...
Homework Statement
Hello today I am solving a problem where an electron is trapped in a potential well. I have a solved Schrodinger's Equation. I am having problems in figuring out what the wave function should be. When I solved the equation I got a complex exponential. I know I cannot use the...
1. Homework Statement
Consider a potential field
$$V(r)=\begin{cases}\infty, &x\in(-\infty,0]\\\frac{\hslash^2}{m}\Omega\delta(x-a), &x\in(0,\infty)\end{cases}$$
The eigenfunction of the wave function in this field suffices...
Consider a potential cavity
$$V(r)=\begin{cases}\infty, &x\in(-\infty,0]\\\frac{\hslash^2}{m}\Omega\delta(x-a), &x\in(0,\infty)\end{cases}$$
The eigenfunction of the wave function in this field suffices
$$-\frac{\hslash^2}{2m}\frac{d^2\psi}{dx^2}+\frac{\hslash^2}{m}\Omega\delta(x-a)\psi=E\psi$$...
Homework Statement
Given:
Ψ and Φ are orthonormal find
(Ψ + Φ)^2
Homework Equations
None
The Attempt at a Solution
Since they are orthonormal functions then can i do this?
(Ψ + Φ) = (Ψ + Φ)(Ψ* + Φ*)?
Homework Statement
Homework Equations
where
The Attempt at a Solution
I tried to integrate (7-32) over all values of r (i.e., from negative infinity to positive infinity) and set it equal to 1, but the result was too messy and was divergent. Am I making the right approach?
Homework Statement
Find the noralization constant ##A## of the function bellow: $$ \psi(x) = A e^\left(i k x -x^2 \right) \left[ 1 + e^\left(-i \alpha \right) \right], $$ ##\alpha## is also a constant.
Homework Equations
##\int_{-\infty}^{\infty} e^\left(-\lambda x^2 \right) \, dx = \sqrt...
I just confused about it.Why can't we discribe a particle just one wave function instead of wave packet(group of waves with different phase velocities)?
Hi.
A beam of previously unpolarized or diagonally polarized doesn't create an interference pattern behind a double slit if there is a vertically and horizontally oriented polarizer behind either slit.
The classical explanation is that the electric field is a vector perpendicular to the...
The question is as follows:
A particle of mass m has the wave function
psi(x, t) = A * e^( -a ( ( m*x^2 / hbar) +i*t ) )
where A and a are positive real constants.
i don't know how to format my stuff on this website, so it may be a bit harder to read. Generally when i write "int" i mean the...
The question is;
In an experimental small universe, a photon is released from a source. It continues its path as a probabilistic wave function. if it interacted with mass, we could say the wave function collapsed and observe a particle photon hitting an object.
But what happens when the photon...
Homework Statement
The fourier transfrom of the wave function is given by
$$\Phi(p) = \frac{N}{(1+\frac{a_0^2p^2}{\hbar^2})^2}$$
where ##p:=|\vec{p}|## in 3 dimensions.
Find N, choosing N to be a positive real number.
Homework Equations
$$\int d^3\vec{p}|\Phi(p)|^2=1$$
, over all p in the 3...
Homework Statement
$$\Psi = Ae^{\frac{i}{\hbar}(px-\frac{p^2}{2m}t)}$$
where ##p = \hbar k## and ##E = \hbar \omega = \frac{p^2}{2m}## for a nonrelativistic particle.
Find ##\Psi'(x',t')##, E' and p', under a galilean tranformation.
Homework Equations
$$\Psi'(x',t') = f(x,t)\Psi(x,t)$$
where...
If a wave function could be assigned to a whole galaxy, would its mass spread along the wave? Could this account for the anomalies in our calculations for galactic spin?
Homework Statement
Find the wave packet Ψ(x, t) if φ(k) = A for k0 − ∆k ≤ k ≤ k0 + ∆k and φ(k) = 0 for all other k. The system’s dispersion relation is ω = vk, where v is a constant. What is the wave packet’s width?
Homework Equations
[/B]
I solved for Ψ(x, t):
$$\Psi(x,t) =...
I would like to get your ideas on what Australian professor at ANU David Chalmers' proposes that consciousness arises out of certain configurations of complex states (Integrated information theory) and then the existence of that consciousness collapses the wave function. Specifically, why isn't...
Is there a difference between Schrodinger's equation and the wave function? In the beginning of the second edition by David J. Griffiths he compares the classical F(x,t) and Schrodinger's equation and I am having trouble understanding the connection.
Homework Statement
I have the wave function Ae^(ikx)*cos(pix/L) defined at -L/2 <= x <= L/2. and 0 for all other x.
The question is:
A proton is in a time-independent one-dimensional potential well.What is the probability that the proton is located between x = − L/4 and x = L/4 ?
Homework...
Hi,
I am going around in circles, excuse the pun, with phasors, complex exponentials, I&Q and polar form...
1. A cos (ωt+Φ) = Acos(Φ) cos(ωt) - Asin(Φ)sin(ωt)
Right hand side is polar form .... left hand side is in cartesian (rectangular) form via a trignometric identity?
2. But then...
So there's a free particle with mass m.
\begin{equation}
\psi(x,0) = e^{ip_ox/\hbar}\cdot\begin{cases}
x^2 & 0 \leq x < 1,\\
-x^2 + 4x -2 & 1 \leq x < 3,\\
x^2 -8x +16 & 3 \leq x \leq 4, \\
0 & \text{otherwise}.
\end{cases}
\end{equation}
What does each part of the piecewise represent...
Homework Statement
Show that the displacement D(x,t) = ln(ax+bt), where a and b are constants, is a solution to the wave function.
Homework Equations
I'm not sure which one to use:
D(x,t) = Asin(kx+ωt+φ)
∂2D/∂t2 = v2⋅∂2D/∂x2
The Attempt at a Solution
I'm completely lost on where to start...
Homework Statement
Show that the normalized wave function for a particle in a three-dimensional box with sides of length a, b, and c is:
Ψ(x,y,z) = √(8/abc) * sin(nxπx/a)* sin(nyπy/b)* sin(nzπz/c).
Homework Equations
Condition for the normalization:
∫0adx ∫0bdy ∫0cdz Ψ*(x,y,z)Ψ(x,y,z) = 1...