Question

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 wavefunction, E is the energy, m the mass and x represents the position of the particle in the box. Application of appropriate boundary conditions, leads to wavefunction of a particle in a one-dimensional box of length L given by equation (2), v (x)= N sin( 67%), Where n = 1, 2, 3, .. and y(x) is the wavefunction as a function of position x and quantum number, n. N is a normalisation constant. The standard integral for the term sin? (ax) is given below, ſsin? (ax) dx = - sin(2ax)+C. (3) 2 4a Using equation (3) determine the form of the normalisation constant, N. Thereby rewrite equation (2) to provide the complete description of the wavefunction of a particle in a box.

Answer 1

CZ | We hares Given wave finition Yews N8m/nan) eue hascite for å normalisahon factor No use knew that.' Yesss You You a probability Density The Ameability of finding a pastele bleve all of the space should sub upken 1 Lyrius Yeas du=17 Pese particle_id located blus neo_douch; Therefore 6 Iramaques ] [a banqx33 die = 2 N" ["Sm?(nqu3 de z 1 Using-fsm?comida e - Sin (2010) + c N° [ . - thansen (29,7x)} = 1 ft L-0221 NE o 22 JEsan (max 2 Ales Seemmed wip) FASE LIKE IF THIS WAS HELPFULI CamScannelle