Discussion  Fr 11.11.2005 at 12:15,  HR 30.1

Home work 2
 
 

Exercise 1:  A particle in a one-dimensional box

An electron is captured in a one-dimensional box of length a=20 Angström (2 nm).

a. Using the Schrödinger equation within that box (V = 0 for 0 £ x £ a; V = ¥ elsewhere) calculate wavefunctions Y_n and the energy eigenvalues E_n using the appropriate boundary conditions. You should come out with the formulas were given at the lecture.
b. You know that the probability density to find the electron with the coordinate x in the potential box is |Y_n(x)|². Using the known wavefunction calculate the probability of finding the electron in the states with n=0 and n=1somewhere between x = 0.25a and x=0.75a.        
 

Exercise 2:  Harmonic oscillator

You know that the energy states of the harmonic oscillator is described by the expression E_v=(v+1/2)hν, where ν = 1/(2p)(k/m)^1/2. Using the force constant for HCl molecule  k = 516 N m^-1 and the Planck formula, calculate the wavelength λ of the radiation which is needed for exciting transitions between the HCl vibrational energy levels and conclude which spectral region this radiation belongs to.     

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