Question

Transcribed Image Text:Consider a particle in a box with edges at x = ±a .
Estimate its ground state energy using variational
method with the trial function
w = |x|* – a²
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 2 steps

Knowledge Booster
Similar questions
- An electron is confined to a potential well of width 0.350 nm. (a) Find the ground-level energy E1-IDW if the well is infinitely deep. If instead the depth U0 of the well is six times the value of E1-IDW, find (b) the ground-level energy and (c) the minimum energy required to free the electron from the well.arrow_forwardYou want to determine the possible energy observable values of a particle in a non- zero potential described by a wave function. Which of the following equations represents that process? ħ² 2m ·V² + V| y = 0 +17] 26 οψ ħ² [2²] =0 &= 04 2m – iħ√y = oy xy = 06arrow_forwardAn electron is trapped in an infinitely deep one-dimensional well of width 10 nm. Initially, the electron occupies the n = 4 state. Suppose the electron relaxes to ground state with the accompanying emission of a photon. Calculate the energy of the photon.arrow_forward
- Solve the time-independent Schrödinger equation and determine the energy levels and the wave function of a particle in the potential a? V (x) = Vol a + 2r2 with a = const.arrow_forwardThe wave function of a particle in a one-dimensional box of width L is u(x) = A sin (7x/L). If we know the particle must be somewhere in the box, what must be the value of A?arrow_forwardAn electron is trapped in a region between two infinitely high energy barriers. In the region between the barriers the potential energy of the electron is zero. The normalized wave function of the electron in the region between the walls is ψ(x) = Asin(bx), where A=0.5nm1/2 and b=1.18nm-1. What is the probability to find the electron between x = 0.99nm and x = 1.01nm.arrow_forward
- a question of quantum mechanics: Consider a particle in a two-dimensional potential as shown in the picture Suppose the particle is in the ground state. If we measure the position of the particle, what isthe probability of detecting it in region 0<=x,y<=L/2 ?arrow_forwardShow that normalizing the particle-in-a-box wave function ψ_n (x)=A sin(nπx/L) gives A=√(2/L).arrow_forwardA particle is in the ground state of an inifite square well with walls at x = 0 and x = a. Suddenly the right wall moves from x = a to x = 2a. If the energy of the particle is measured after the wall expansion, what will be the most probable value of the probability of getting this resultarrow_forward
arrow_back_ios
arrow_forward_ios