Potential well Definition and 218 Threads

if V is reduced to much smaller than the zero point energy then what happens to the ground state and first excited state? for this i know that the function becomes continuous and that the particle is unbound. does this mean that the function will also just have an oscillatory form?

Homework Statement Show that the TISE expression you found in part (a): I found it (a) to be: \frac{d^{2} \psi}{dx^{2}} - \frac{2m}{\hbar ^{2}}(e \xi x - E) \psi (x) = 0 Show it (a) can be simplified to: \frac{d^{2} \psi}{dw^{2}} - w \psi = 0 Homework Equations w = z - z0...

For the second, third, fourth, and fifth levels of the three-dimensional cubical box, find the energies in terms of the quantity Eo=π2*h2/(2mL2), where m is the particle mass and L is the box's sidelength.

ok so i have a question on infinite potential wells... if you have the energy state when n=3, does that mean that you have to have the energy state when n=2 and n=1? Ok basically the Q we are given is: A particle of mass m is trapped in an infinitely deep one-dimensional potential well...

This question came up in another thread I started about the wave functions of helium vs hydrogen. It's gone off on something of a tangent so I hope I'm not out of line in starting a fresh thread with this topic. I've basically sketched what I would think are the only two realistic candidate...

Rectangular Potential well if hbar --> 0 Hi, I have a very simple question: My professor said that if \hbar \rightarrow 0 in the transmission coefficient does not yield 0 (case E < V0) as classical results would expect. I think the correct transmission coefficient is solved in Wikipedia...

Particle in a potential Well interacts with the wall without touching it? The ground state Energy for a particle in an infinite potential well is given by E = h2 / 8mL2 Consider a particle with high mass, say 1 kg. Then the ground state Energy will be very very low. So the velocity of the...

For a particle in finite potential well we can have several bound states depending on the height of potential well. Each bound state corresponds to definite energy En. Then corresponding to Each definite Energy there should be definite Momentum Pn. Since we have definite momentum--->...

Homework Statement Show that the conditions for a bound state, Eqn1 and Eqn2, can be obtained by requiring the vanquishing of the denominators in Eqn3 at k=i\kappa. Can you give the argument for why this is not an accident? Homework Equations Eqn1: \alpha=q*tan(qa) Eqn2...

How does energy become quantized in an infinite potential well??

Hello, As we know, the wave function of infinite potential wells form a complete orthogonal base. I have tried now to solve out the wave function for finite potential well, checking the orthogonality, I found that they are no longer orthogonal to each other (I mean the wave function...

Homework Statement A particle of mass m moves in one dimension in the following potential well: V(x)=infinity, x<0 , x>L/3 V(x)=0 , 0<x<L/3 a)Circle the general functional form of the 1st excited wave function phi_1(x) in the region 0<x<L/3. k is a positive constant; A is constant as well...

infinite potential well and the uncertainty principle the solution for Schroedinger equation in infinite potential well satisfy the following energy levels: where l is the width of the well. E can't be zero since then \psi=0 so there isn't any particle in the well . i read in...

Hi! Let's suppose an electron in a mono-dimensional potential well. According to Heisenberg uncertainty principle, if L is the length of the well, then I have a momentum greater than \frac{h}{L}, which means that the electron has a velocity (and so a kinetic energy) greater than \frac{h}{L*m_e}...

Homework Statement The nth energy level for a particle of mass m confined in an infinite potential well is given by: where L is the width of the well and h is Planck’s constant. Assuming that the uncertainty in the particle’s momentum is equal to the momentum itself, show that the...

This question was posed to me a while ago, but I never fully understood how to solve it. You have a particle in the first excited state of the infinite square well (with the origin taken to be at the center. You "abruptly" change the shape of the potential well to be that of the harmonic...

I was working through the textbook and it just gave the solutions to the potential well barrier as in [B/A]*2 and [F/A]*2 and T i was trying to figure it out with the conditions but couldn't get the answer i have attached the conditions, can some one show me how to find these values from the...

This is more a qualitative question than a specific homework question, but a homework problem got me wondering about it. I was solving the finite potential well. V(r) = 0 \hspace{1cm} r \geq a V(r) = -V_0\hspace{1cm} r < a I am trying to solve for the ground state energy. When I find...

Hi, I have learned the Dirac equation recently and I managed to solve it for a free particle (following Greiner book “relativistic quantum mechanics” and Paul Strange book “Relativistic Quantum Mechanics”). I was asked to solve the Dirac equation in the stationary frame for a free particle (no...

Homework Statement Consider a particle in a potential ; V(x)=0\ for\ 0<=x<=L and V(x)=\infty\ otherwise . Its wave function is a linear superposition of the lowest two stationary states and given by \psi(x,t)=\frac{1}{2}*(\sqrt{3}...

Homework Statement A particle is trapped in an infinite potential well, with the infinite walls at ±a. At time t=0, the wavefunction of the particle is \psi = \frac{1}{\sqrt{2a}} between -a and a, and 0 otherwise. Find the probability that the Energy of the particle is \frac{9...

The following Wolfram web page shows the probability density functions for two identical bosons in a square potential well. It also shows the probability density for two identical fermions. http://demonstrations.wolfram.com/WaveFunctionsOfIdenticalParticles/ So it appears that each is...

Homework Statement Does anyone now how to solve the schrodinger equation for a potenital such that: V1(0<x<a), v2(a<x<b), v3(b<x<c). Also i need to write down the condition which gives the possible energy eigenvalues of a particle in the potential. ITs easily to solve the first potential well...

Homework Statement An infinite potential well with a box in the middle V = 100, the walls of the box go from -L/2 to L/2. Homework Equations Schrodinger's equation. The Attempt at a Solution Please help.

Homework Statement An electron is in a Infinite potential well (1-dimensional box with infinite wall boundary conditions) at the second energy level. The width of the box is L. What is the electron density n(x) as a function of the position x? Homework Equations time-independent Schrödinger...

Homework Statement A Spherical potential which is 0 for 0<r<a Vo for r>a Find the condition for bound states, for the radial function with l=0 Plot the result.The Attempt at a Solution I have gotten the equation - tan(ka)=k/lambda where k is the wavenumber for the wave inside the well and...

The task is to find a wavefunction (doesn't need to be normalised) and the energy levels of a particle in an asymmetric potential well (a Schrodinger problem). i.e V = V1 for x<0, 0 for 0<x<d and V = V2 for x>d. What I've got so far is Let α^2= 2m (E-V1)/ℏ^2 β^2= 2mE/ℏ^2...

Hi, I have learned about the infinite quantum well last week and today the finite quantum well was introduced. There is however one thing I don't completely understand, or which I'm not completely happy with. In the case of the finite well, the shrodinger equation is solved for both inside...

Hφ(x) =((p2op)/2m + V(x))φ(x) = (-hbar2/2m.d2/dx2+ V(x)φ(x) = E φ(x) This equation is supposed to relate to an electron confined in a one-dimensional potential well. I'm really confused about where it comes from and I do not know what V(x) represents. If anyone could help explain this...

Homework Statement consider the scattering matrix for the potential 2m/hbar2 V(x) = λ/a δ(x-b) show that it has the form (2ika/(2ika-λ) , (e-2kib) λ/(2ika-λ) (e2kib) λ/(2ika-λ) , 2ika/(2ika-λ) (I've used commas just to separate terms in the matrix) prove...

Homework Statement Find the wave function of particle in a 1-dimensional potential Well of length L, n=2 and mass m Homework Equations I think this would be the wave equation, but not 100% sure [tex]\varphi=Asin(n\pix/L)[\tex] where n=1,2,3... tex doesn't work for me---=Asin[n*pi/L] The...

Homework Statement An experimental physicist submits a proposal to a granting agency requesting support to construct an infinite potential well analogous to the one shown in Figure 3.5 (an electron trapped in a one dimensional box made of electrodes and grids in an evacuated tube)...

Homework Statement Consider a particle confined in a 1D potential well of length L. Derive the normalized wavefunctions and energies of the eigenstates of the system in terms of the quantum number n, working from the time independent Schördinger equation. With the particle initially in the...

1.in the attached file see the fig 8.5 What is the the physical reason,for which ahe amplitude of the wave function is larger in between x=0 & x= a ? 2.what is the reason for choosing a wave packet to describe a particle ?

Problem Given that \frac{2ma^2 |V|}{\hbar^2} = \left(\frac{7\pi}{4}\right)^2 for an electron in a potential well of depth |V| and width 2a = 10^{-7} \text{cm}, if a 100\text{-keV} neutron is scattered by such a system, calculate the possible decrements in energy that the neutron may...

What does a particle in a potential well means? What is the physical interpretation of it? Could anyone anser this topic

If you think this will get more replies in the intro phys please let me know and i will move it: A particle of total energy 9Vo is incident from the -x axis on a potential given by: V \left\{8Vo, x<0\right\} \left\{0, 0<x<a\right\} \left\{5Vo, x>a\right\} Find the probability that the...

I know this question seems very simple which is why its bugging me so much: Why is the ground state energy not zero? A simple answer would be greatly appreciated

I've got this question and I'm absolutely clueless, any help will be greatly appreciated: The nth energy level for a particle of mass m confined in an infinite potential well is : E = h^2n^2/8ml^2 where L is the width of the well and h is Planck’s constant. Assuming that the uncertainty...

d) Show that the eigenvalues of a particle in a well aren’t affected by the structure of the bottom of the well by applying perturbation theory. As an example, investigate the case where the bottom of the well is deeper in the middle (x = a2) than at the sides (x = 0 and x= a). To do this:- i...

I've been meaning to ask this question for a while but I thought I'd google it first. I found out that this question was put to this forum a few years ago by peter038, without a definite resolution. So I thought maybe we could try again. Part of the problem is to decide exactly what is the best...

Homework Statement A potential well with V(x)=0 for x<0 and V(x) = Vo for x>0. The particle has energy E greater than Vo and is incident from the left side. Calculate the reflection coefficient. Homework Equations Relfection coefficient is given by R= (B*B)/(A*A) The Attempt at a...

hi, I am not getting idea to solve below problem A particle of mass m is in a one-dimensional ,rectangular potential well for which V(x)=0 for 0<x< L and V(x)=infinite elsewhere. The particle is intially prepared in the ground state ψ1 with eigen energy E1. Then , at time t=0, the potential...

Homework Statement I am to calculate the number of states in a 3Dcubic potential well with impenetrable walls that have energy less than or equal to E Homework Equations \ E_n=\frac{\hbar^2\pi^2}{\ 2 \ m \ a^2}\ (\ {n_x}^2 + \ {n_y}^2 + \ {n_z}^2) The Attempt at a Solution We may...

[SOLVED] Heisenberg and energy of an electron in a potential well Homework Statement An electron is confined within a one dimensional potential well that measures 1 nm. using the uncertainty principle, estimate the order of magnitude for the ground state energy of the electron in the well in...

[SOLVED] Energy in a Potential Well I so need help with this! "The width of a one-dimensional potential well of an electron can be assumed to be about 2 A (there's a weird-looking bubble on top of the A). Calculate the energy of an electron (in Joules and in eV) from this information for...

I've been told about the infinite potential well using quantum-mechanics, with mathematical proof. Is there any websites I can look at to understand this theory with less math, but instead, with a theoratical approach? Would classical-physics be able to describe this result? thanks

I remember this homework assignment I did a while back, where we "found" the wave function of a particle in a double potential well. The distance between them was variable and we found that as the distance decreased, the energy of the system went down. This would suggest a force pulling the...

Homework Statement Hi, Particle of mass m is found in one-dimensional infinite potential well with walls 0<=x<=a. In t=0 the normalized wave function is: \psi(x,t=0)=A[1+Cos(\frac{\pi x}{a})]Sin(\frac{2 \pi x}{a}) find psi(x,t) Homework Equations ? The Attempt at a Solution...

I do still not understand definition of potential well. Could you help me answer this question? What is the meaning of Potential well in modern physics? What is difference between Potential well in modern physics and classical physics?