# Solution to the T.I.S.E

1. Dec 29, 2006

### repugno

What is the physical interpretation of the imaginary component in the spherical harmonics? I am under the impression that when we sketch the shapes of the spherical harmonics we exclude the imaginary components.

2. Dec 29, 2006

### StatMechGuy

We typically do. The wave function itself has no physical interpretation, merely its modulus squared, so by itself the imaginary part is of no physical consequence.

In fact, one can show that the eigenstates of a hamiltonian can always be chosen to be real.

3. Dec 30, 2006

### repugno

When we take the modulus squared of the spherical harmonics we loose the term containing the azimuth angle and the imaginary number. Isn't this a problem since we loose information about the shapes?

4. Dec 30, 2006

### Dr Transport

The imaginary part of the harmonic is a phase function.

5. Jan 3, 2007

### dextercioby

Consider it a price to be payed in order to keep the theory consistent. As already stated, for pure states phase factors are factorized through.

Daniel.