Potential well Definition and 218 Threads

Hello I read the following sentence when reading about ion traps: "By changing the trapping voltage we are changing the depth of the potential trapping well, therefore at the same axial position there is a corresponding increase in the potential well, which means that the ion will have to...

Homework Statement It's problem on the uncertainty principle. It is as follows: Suppose we have confined an electron in an infinite potential well of length L=1A . Say that this electron is in the ground state of the well. Now, say that we wish to observe the electron with accuracy of 0.2A...

Homework Statement ψx is the function of postion for a particle inside a 1D finite square well. Write down the expression for finding the particle a≤x≤b. Do not assume that ψx is normalised. Homework Equations The Attempt at a Solution This is to check I'm not going insane: P...

Homework Statement A particle of mass (m) moves in the one-dimensional potential V(x) = V0 0 ≤ x ≤ a = ∞ otherwise Wave function of the particle is ψ(x,t) = C sin (\frac{x\pi}{a}exp[-iωt] Determine V0 Homework Equations Schrödinger's Equations...

Homework Statement find Transmission and Reflection coefficients (QM) for the following triangular potential well: U=U_{0}(1-\frac{x}{a}) : x\geq0 and U= 0 : x<0 and U_{0}>0 , a>0 Homework Equations The Attempt at a Solution Basically constructing the wave functions is...

Homework Statement A particle of mass m is confined (in one dimension) to the region 0 ≤ x ≤ a by a potential which is zero inside the region and infinitely large outside. If the wavefunction at time t = 0 is of the form ψ (x,0) = Ax(a - x) inside the region ψ (x, 0) = 0 outside the...

I was wondering why the spacing between energy values keep increasing for the infinite potential well?

hey, say you have a infinite potential well of length L, in the middle of the well a potential step of potential V and length x. Inside the well is a particle of mass m. why are the first order energy corrections large for even eigenstates compared to odd ones? also, say well...

Homework Statement For the case n=1, calculate the probability that the particle is found in within the region a/4<x<3a/4 (n is the energy level, a is the width of the infinite potential well). Compare this result with the case n=8 and with the classical result. Homework Equations...

Hey, I've been trying to work out how, for a finite well of high Vo and width L, the interior solution has the form L Sin(kx + d), I see that if d=0 then the solution resembles an infinite well, so that implies d depends inversely on the wells potential. But I can't work out what d comes...

http://img138.imageshack.us/img138/7762/asdhl.jpg Thanks in advance

Homework Statement The deuterium nucleus (a bound state of a proton and a neutron) has one bound state. The force acting between a proton and a neutron has a strong repulsive component of range 0.4 fm and an attractive component of range ~2.4 fm. The energy needed to separate the neutron from...

if ψ=C*e^(kx) + D*e^(-kx) show that the probability current density is Jx=(i*k*hbar/m)[c*conj(D) - conj(C)*D] since Jx= (i*hbar/2m)*[ψ * derivative of conj(ψ) - conj(ψ)*derivative of ψ] ψ=C*e^(kx) + D*e^(-kx) conj(ψ)= conj(C)*e^(-kx) + conj(D)*e^(kx) ψ ' = C*k*e^(kx) - D*K*e^(-kx)...

Homework Statement Particle is in a potential well in the shape of a isosceles right-angled triangle. Need to find the wave function and allowed energies. Homework Equations How to determinate a boundaries for the potential when that line is in a form of some linear function, there is no...

an electron in a potential well of thickness (e.g 1nm) with infinitly high potential barriers. it is in the lowest possible energy state. to calculate the energy of the electron. i used: E=(n^2 pi^2 h(bar)^2)/ (2m Lz^2) which will result in approx 10E-19 j my question is, how can...

Hi PF users, The subject of this thread is clearly stated on the title ( above). So my question is what is mean't by a 'potential well'. I have a question based on Lennard jones potential from where this question arose in the first place ( which I will probably post on respective...

If I have a low energy neutron and I bring it close to a nucleus it will be captured when it gets close enough. How can I calculate the shape of the potential well of the nucleus for neutron capture? I keep reading that it is due to the strong force, which I agree with. But it is some...

Homework Statement An electron enters in a finite rectangular potential well of length 4 angstroms. When the entering electrons have a kinetic energy of 0.7 eV they can travel through the region without having any reflection. Use this information to calculate the depth of the potential well...

Homework Statement Consider a potential well with infinite high walls, i.e. V(x)=0 for -L/2\leq x \leq +L/2 and V(x)=\infty at any other x. Consider this problem (the first task was to solve the stationary Schroedinger equation, to get the Energies and Wave Functions, especially for n=1 and...

Homework Statement "Use the semi - infinite well potential to model a deuteron, a nucleus consisting of a neutron and a proton. Let the well width L be 3.5 x 10^-15 meters and V - E = 2.2 MeV. Determine the energy E, and determine how many excited states there are."Homework Equations Since V >>...

Imagine you put a sphere on a track which is part of a vertical circle.You expect the sphere to roll in a path like a pendulum.it should do it like a mass on an almost frictionless surface because the friction of the surface is rolling the sphere not stopping it and the air drag isn't very high...

Homework Statement particle moving in the semi infinite potentail well set up and solve SE for the system assume E<VoHomework Equations (-h2/2m) d2\psi/dx2 +v(x)\psi=E\psiThe Attempt at a Solution so in reagion one its infinite so \psi=0. reagion 2 is what i am confused about. looking throught...

Homework Statement So, I'm asking for a bit of help before I confuse myself completely. The question statement is: Consider a two-dimensional potentialbox V(x,y) = 0 if 0 \leq x \leq a, 0 \leq y \leq 2a and infinity otherwise. a) Determine the energy eigenstates and energy...

Hello, can anyone explain the full analysis of finite square potential well (bound state and scattering state) if V(x) = -Vo, x <= 0 (region 1) V(x) = 0, 0 < x < a (region 2) V(x) = -Vo, x >= a (region 3) It will be helpful if you can attach the analysis in .pdf format. Thank you in...

Homework Statement A particle of mass m is find to be inside a uni-dimensional potential well of the form: V(x)=0 for x \leq -a and a\leq x and V(x)=-V_0 for -a <x<a. 1)Write down the corresponding Schrödinger's equation. 2)Consider the case -V_0<E<0. Determine the contour conditions and...

Hello forum, I have a question regarding the delta function potential well. Given the following potential: V(x) = -αδ(x) for -a/2 < x < a/2 (α- positive constant) and V(x) = 0 elsewhere, how would one show that the ground state is the only eigenstate with E <0. One could of course solve the...

Homework Statement 1)The graph below represents the ground state wave function of an electron in a finite square well potential of width L. The potential is zero at x = 0. The wave function of the electron within the well is of the form A cos( 2πx / λ ) where A is a normalization...

Hello again. Thank you guys. You have been great help... I have another one: Given a potential well- 2a is it's width, and in the middle - there is a delta potential: V(x)= \frac {\hbar^2} {2m} \frac {\lambda} {a} \delta(x) I am looking for the odd solution to this problem. I thought...

Homework Statement 1.) A particle of kinetic energy 50 eV in free space travels into a region with a potential well of depth 40 eV. What happens to its speed? a.) it stays the same b) it increases in the region of the well c) it decreases in the region of the well d) not enough information...

Homework Statement Hi guys, I'm having trouble understanding the finite potential well, in particular the boundary conditions The well under scrutiny has potential V(x)= 0 for |x|<a and V(x)=V_0 for >a Homework Equations \frac{d^2\psi}{dx^2}=-\sqrt{\frac{2mE}{\hbar^2}}\psi=-\alpha^2\psi...

Homework Statement If you have a 1d infinite potential well between 0 and a which is then expanded to become 0 -2a with the wavefunction in that instant undisturbed, what is the expectation value of energy at that moment. my thoughts are that as the eigenfunction will be the same then...

Hello Again! My question: Find the bound energy spectrum of the potential that contains two delta-function wells: V(x) = -V_{0}\delta(x-\frac{a}{2}) -V_{0}\delta(x+\frac{a}{2}) under the assumption that the wells are located very far away from each other. Find and plot the associated stationary...

Homework Statement See figure attached. Homework Equations The Attempt at a Solution What condition must be satisfied in order for the electron to pass over the well? Thanks again!

problem is: (a)write down the spatial or orbital for two-non interacting particles, with the same mass, in a one dimensional well, where the potential energy is zero for 0<x<2a and infinite anywhere else. (b)What are the energies of the four lowest energy levels for the system in units of...

Homework Statement An electron is confined to an infinite potential well of width L. Find the force it exerts on the walls of the well in the lowest energy state: a) Estimate the force using uncertainty principle b) Calculate the force exactly for the ground-state wavefunction Homework...

By considering the wavefunctions within the potential described below, determine the incident, reflected and transmitted amplitudes of each part of the wavefunction at the step boundary (as necessary). For x<0, V = infinity. For 0<x<a, V = 0 For a<x<L, V = V1 For x>L, V = infinity...

Homework Statement The degeneracy of the nth level above the ground state for a three dimensional harmonic oscillator is (n+1)(n+2)/2 where n takes values n=0,1,2,... A gas of N non-interacting identical lithium atoms (mass 6amu) each having spin1/2 is confined in a 3d harmonic potential...

Homework Statement The problem is to find a well's depth Vo that the electron which is trapped inside has two stable states. Well starts at x=0 and ends at x=L. Homework Equations The Attempt at a Solution I tried to solve Schrödinger equation for each area (x<0 0<x<L x>L) but...

Homework Statement What fraction (as a percentage) does the n=(2x2-1)th infinite potential well wavefunction contribute to the 'classical' initial wavefunction psi(x,t=0)=1/sqrt(L) ? (Why are the even n excluded?) Homework Equations psi(x,t=0) = 1 / sqrt(L) The Attempt at a Solution...

Hi all just a question about the understanding of the solutions of a spherical potential well. What is the physical sense of solutions which have no spherical symmetry? I just would think that the probability of finding a particle whose state is described by one of the eigenstate of the...

Let's imagine an electron that lives in an one dimensional world where there is a potential well near x=0 and that for x=+inf or -inf the electron is free. Is there any relation between the transmission coefficient of an electron arriving at the well coming from x=-inf and the transmission...

Homework Statement A particle in the infinite potential well in the region 0 < x < L is in the state \psi(x) = \begin{cases} Nx(x-L) & \text{ if } 0<x<L \\ 0 & \text{ if } otherwise \end{cases} a) Determine the value of N so that the state is properly normalised b) What is the...

Homework Statement A particle of mass m and total energy E < 0 is confined to a potential given by: where \alpha is some positive constant. Show that the wavefunction is a solution of the time independent Schrodinger equation when x > 0. Find the associated energy Eigenvalue E.Homework...

Homework Statement A particle in the harmonic oscillator potential is in the first excited state. What is the probability of finding this particle in the classically forbidden region? Homework Equations probability of finding particle = integral of abs[psi squared] [a,b] The Attempt...

Homework Statement This is a problem from Merzbacher. Assuming a particle to be in one of the stationary states of an infinitely high one-dimensional box, calculate the uncertainties in position and momentum, and show that they agree with the Heisenberg uncertainty relation. Also show that...

I was curious what a delta-function potential barrier would do to a free (E>0) 1-dimensional particle, so I figured it out. I used V = b δ(x) for the potential energy. I got the expected result that full reflection will occur as |b|→∞ or as E→0. These results make sense intuitively when b>0. My...

What is "excursion" of a potential well? I think it means maximum depth of the well, but I've never heard this term before and I might be wrong. I don't have much of a quantum mechanics background. Details: I'm reading and implementing "Solution of the Schrodinger Equation by a Spectral...

I am trying to derive an equation of motion for a simple electrostatic potential well. Imagine a scenario where an electron (or other charged particle) is released from an arbitrary distance from a fixed (unperturbable) attractive charge (say a proton fixed in space). In 1 dimension, the...

Homework Statement V(x) = \left\{\infty \textrm{ for } x<0 \left\{0 \textrm{ for } 0<x<a \left\{V_0 \textrm{ for } a<x<a+2b \left\{0 \textrm{ for } a+2bx<2a+2b \left\{\infty \textrm{ for } 2a+2b<x Set up the relevant equations in each region, write down the appropriate solution and...

Hi, (first ever post) I have the following three problems 1) A particle is in the ground state of an infinite well from 0<x<a. Find the probability that it is in the middle half of the well. I think I have managed this, its just the integral of the wave function squared then I put in the...