[Glare]

1. The (psi)v describe states of the harmonic oscillator, following is not true about the integral   for the harmonic oscillator
a. This integral is zero.
b. It represents average value of the position coordinate in the state v=2.
c. It is equivalent to the following integral expressed in a dimensionless coordinate y=x/a (a-constant)  
d. It is the transition moment for a transition between two states of the harmonic oscillator: v=2 and v=3.


2.   Nodal surface is best described as a surface
a.   where the wavefunction approaches ∞
b.   across which a particle does not move
c.   separate the regions of different sign for wavefunction
d.   where the kinetic energy of a particle is zero


3.   The following quantum case has energy levels which are equally spaced:
a.   hydrogen atom
b.   particle in a one-dimensional box of final length L
c.   harmonic oscillator
d.   rigid rotor


4.   The wavenumber of a photon of radiation which corresponds to a transition between two levels of a harmonic oscillator is  =500 cm-1.  If the mass of the oscillator is doubled the wavenumber will be about
a.   the same
b.   2 v
c.    v/2
d.    v/(2^(1/2))

5.   Quantum mechanical particle can penetrate classically forbidden regions, which are the areas where
a. classical potential energy is positive   
b. classical kinetic energy is positive
c. classical total energy is zero   
d. classical kinetic energy is negative

6.   The following is not true the quantum-mechanical description of angular momentum
 
a.   an angular momentum vector can have length equal to zero
b. any two components of angular momentum vector can be simultaneously determined
c.   the length of angular momentum vector and its projection on the z-axis are quantized
d.   there are 2l+1 possible orientations of angular momentum vector with respect to the z-axis


Do what you could.. I'm stuck on these problems. I got the other 14 problems though.

[Borek]

Please read forum rules.

[leela sriram]

4> wave number v1=v/(2^1/2)
5>classical KE is -ve
6>[Lx,Ly]=iLz   , [Ly,Lz]=iLx   ,   [Lz,Lx]=iy      so no two components of angular momentum operator can be measured simaltaneously
3>in harmonic oscillator the difference between any two energy levels is same
2>region separating different signs of a wave function
and some times nodal region is a region through which classical particle cannot move
a qM particle can pass through nodal tregion
1>i think some thing is missing in question