Particle in a box Definition and 20 Threads

I have a question about one of the steps in the calculations. For context about where in the calculations I am, we assume that a particle is subjected to a potential energy function that is infinite everywhere along the ##x##-axis except for a line segment of length ##l## where the potential...

I need help .I did not A) E < V0 for T =? (passing coefficient ) B) E = V0 for T = ? C ) E > V0 for T =? A

Homework Statement Hi, I am new to MATLAB and have an assignment where I have to construct a Hamiltonian matrix, apply boundary conditions, then find corresponding eigenvalues and eigenvectors for the electron in a box problem. I am stumped where to start. From our class we learned that you...

Greetings, In the scenario of a particle in an infinite potential well, there are discrete energy levels, i.e.##E=\hbar ^2 n^2 \pi ^2/ (2 m L^2)## where L is the width of the potential well, and n takes on positive integers. But what will happen if I put a particle of energy ##E_i## that is not...

I come across this question in a textbook. Somehow my result is way off from the solution answer. I used the energy formula for particle in a box with n(Initial) = 22 and n(End) = 23, the calculated box length is 732 pm. I arrived at an answer of 39.3 nm. The answer from the answer book is but...

Homework Statement Consider a gas sufficiently diluted containing N identical molecules of mass m in a box of dimensions Lx, Ly, Lz. Calculate the probability of finding the molecules in any of their quantum states. Calculate the energy of each quantum state εr, as a function of the quantum...

Homework Statement Homework EquationsThe Attempt at a Solution ## E \propto n^2 ## ## \frac { \Delta E} E = \frac { 2n +1} {n^2} ## In the limit of large quantum number, ## \frac { \Delta E} E = \frac { 2} {n} ##, option (a).

Homework Statement Homework EquationsThe Attempt at a Solution The energy eigen - value of a particle in a box is given by ## E_n = \frac { n^2 h^2}{8mL^2} ## . Now, applying classical mechanics , ## \frac { p^2}{2m} = \frac { n^2 h^2}{8mL^2} ## . ## p \propto \frac { 1} L ## , So...

<Moved from a technical forum, therefore no template> For two non-interacting fermions confined to a 1d box of length L. Construct the antisymmetric wave functions (Slater determinant) and compare ground state energies of two systems, one in the singlet state and the other in the triplet state...

Hey there, I am familiar with the mathematics of multi-particle systems, but have now moved on to trying to plot them. I was a little ambitious and thought I'd attempt to somehow plot energy eigenfunctions of two particles in a 2-D box. Obviously I immediately ran into the issue that there are...

Homework Statement In a potential box (##L = 1.00pm##) an electron moves at a relativistic speed, meaning it's momentum can't be expressed as ##P = \sqrt{2mE}##. a) Using the uncertainty principle, show that the speed is indeed relativistic b) Derive an expression for the allowed energy states...

Homework Statement Problem: Consider a "crystal" consisting of two nuclei and two electrons arranged like this: q1 q2 q1 q2 with a distance d betweem each. (q1=e, q2=-e) a) Find the potential energy as a function of d. b) Assuming the electrons to be restricted to a one-dimensional...

Considering how Heisenberg's uncertainty principle is applied to a top-hat wave function: This hyperphysics page shows how you can go about estimating the minimum kinetic energy of a particle in a 1,2,3-D box: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/uncer2.html You can also...

Homework Statement a) Determine the ratio (Em/En) between two energy states of a particle in a one dimensional box of length l. b) Show that this is consistent with the non-relativistic low-energy limit. The attempt at a solution I have figured out a) using the de broglie wave-particle duality...

Homework Statement A One dimensional box contains a particle whose ground state energy is ε. It is observed that a small disturbance causes the particle to emit a photon of energy hν=8ε, after which it is stable. Just before emission a possible state of the particle in terms of energy...

For particle in a box with the finite depth, is it traveling wave? or standing wave? I am confused with its ability to pass through the potential walls that is classically forbidden area which makes me think it is traveling wave. But for particle in a box with infinite potential, I understand...

Homework Statement If a one-dimensional box is 1 nm long, what is the probability of finding the particle between the following limits? (a) x = 0 nm and x = 0.05 nm (b) x = 0.55 nm and x = 0.65 nm Homework Equations ψ = (2/L)½ sin(πx/L) The Attempt at a Solution (I do chemistry and I'm really...

If there exists some normalized wavefunction ##\psi## that is not a solution to the Schrödinger equation (1D), what does this mean? You can still presumably use the square of the wave function to ascertain the probability it exists at some interval in space, but does it provide any other useful...

For a particle in a box that is described with a wave function, why can there only be a standing wave when there is an infinite potential well? From my understanding, the infinite potential well makes it impossible for the particle to tunnel through the barrier and so the wave function cannot...

Homework Statement A particle in a box of width 2a is in a state \psi=\frac{1}{\sqrt{2a}} for |x| less than or equal to a and 0 for |x| greater than a. What is the probability of finding the particle in [-b, b] inside the box? What is the probability of finding the particle with momentum p...