Page 1 of 2 Quiz #4 Consider a potential well consisting of an infinite barrier at x < 0 and a finite barrier of height V0 for x > L. The energy E is less than V0. 1. [2 points] What is the general wavefunction solution to the time-independent Schrodinger Equation for the region 0≤≤xL (i.e. before application of boundary conditions)? You should combine several constants into a wavenumber k. 2. [2 points] What is the general wavefunction solution to the time-independent Schrodinger Equation for the region xL> (i.e. before application of boundary conditions)? You should combine several constants into a wavenumber α. Name:_______________________ PHY3101 3/16/01 −∂∂+ =∂∂− + =hhh2 222 222 2m xV x t it mddxV x Eψψψ ψψ ψ( , ) ( ) V xxx LV x L( ) =∞ <≤ ≤>RS|T| 0 000V xaf xL0EPage 2 of 2 3. [2 points] Apply boundary conditions at x=0 and x=∞ to simplify your answers to problems 1 and 2 (i.e. eliminate as many unknown constants as possible). 4. [2 points] Apply boundary conditions at xL= to further simplify the wavefunction solution (eliminate one more constant), and also obtain an equation (don’t solve it!) to relate the constants k and α. 5. [2 points] Sketch the ground state wavefunction solution for this
View Full Document