Make sketches of the first three wavefunctions for the particle in the box. Label both axes and indicate appropriate quantum numbers for each wavefunction.
Make sketches of the first three wavefunctions for the particle in the box. Label both axes...
The following is an acceptable wavefunctions for a particle in a 2D rectangular box with infinite walls: (12 points) 12/ innxx -intnxx\ / innyy -innyy le Lx - e Lx 1 Ly – e Ly Lx 12Ly 16x9 = (+)* (24)*(7*-77)( ) a. Show that this wavefunction is normalized. (hint: you should expand the exponentials into their trigonemtric forms using Euler's formula) b. Show that the expectation value of px is equal to zero. (hint: use the trigonemtric forms again)
3. A particle is in a 1D box (infinite potential well) of dimension, a, situated symmetrically about the origin of the x-axis. A measurement of energy is made and the particle is found to have the ground state energy: 2ma The walls of the box are expanded instantaneously, doubling the well width symmetrically about the origin, leaving the particle in the same state. a) Sketch the initial potential well making it symmetric about x - 0 (note this is different...
Particle in a box Figure 1 is an illustration of the concept of a particle in a box. V=00 V=00 V=0 Figure 1. A representation of a particle in a box, where the potential energy, V, is zero between x = 0 and x = L and rises abruptly to infinity at the walls. The Schrödinger equation for a particle in a box reads t² d²u Y +V(x)y = Ey 2m dx2 + (1) where ħ=h/21 , y represents the...
The wavefunctions for a particle in a box are given by: ψn(x) = (2/L)^1/2 sin(nπx/L), with n=1,2,3,4. . . . Let’s assume an electron is trapped in a box of length L = 0.5 nm. (a) Light of what wavelength is needed to excite the electron from the ground to the first excited state? (b) Will that wavelength increase or decrease, if you exchange the electron with a proton? Why?
2. Derive the wavefunction and the energy of a particle in three dimensional box (expand it from 1)
The wave function given below is suggested to fit the particle in a box of length L in one dimension: Duh!! also known as the particle on a line: V=N (L x-); where N is the normalization constant. Problem One. List three conditions (in a short phrase) that make any wavefunction acceptable. For each condition, show that the above wavefunction satisfies the condition you listed. (Use the allotted spaces below to answer the question). (1) (III).
Give the parities (g,u) of the a) first four levels of a 1D particle-in-a-box wavefunction, and b)the first four levels of the harmonic oscillator.
Q 1: For particle in a box problem, answer the following questions, a) Why n=0 is not an allowed quantum number? b) En = 0 is not allowed for particle in a box, why? c) Ground state wavefunction is orthogonal to the first excited state wavefunction, what does it mean? Q 2: An electronic system that is treated as particle in 3-D box with dimensions of 3Å x 3Å x 4Å. Calculate the wavelength corresponding to the lowest energy transition...
There are four sketches below. The first sketch shows a sample of Substance X. The three sketches underneath it show three different changes to the sample. You must decide whether each of these changes is possible. If a change is possible, you must also decide whether it is a physical change or a chemical change. Each sketch is drawn as if the sample were under a microscope so powerful that individual atoms could be seen. Also, you should assume that...
Given a 3-dimensional particle-in-a-box system with infinite barriers and L-5nm, Ly-5nm and Li-6nm. Calculate the energies of the ground state and first excited state. List all combinations of values for the quantum numbers nx, ny and nz that are associated with these states. Given a 3-dimensional particle-in-a-box system with infinite barriers and L-5nm, Ly-5nm and Li-6nm. Calculate the energies of the ground state and first excited state. List all combinations of values for the quantum numbers nx, ny and nz...