# Tag Info

Accepted

### How should we think about Spherical Harmonics?

How should we think about Spherical Harmonics? In short: In the same way that you think about plane waves. Spherical harmonics (just like plane waves) are basic, essential tools. As such, they are ...
• 125k
Accepted

### What is the difference between a Hilbert space of state vectors and a Hilbert space of square integrable wave functions?

This is a good question, and the answer is rather subtle, and I think a physicist and a mathematician would answer it differently. Mathematically, a Hilbert space is just any complete inner product ...
• 42.6k
Accepted

### How is Pauli's exclusion principle valid for electrons of two hydrogen atoms in ground state, having same spin?

A quantum state includes the information about a particle's position. Two particles with the same quantum numbers at different locations are in different states, so are allowed by the exclusion ...
• 42.6k
Accepted

### Why can't every quantum state be expressed as a density matrix/operator?

The statement by yuggib is correct. To put it in perspective, I'll start with a completely general formulation, and then I'll show how vector-states and density operators fit into that picture. I won'...
• 51.7k
Accepted

### Quantum mechanics and rigorous math

Kets In quantum mechanics the possible states of the system are elements of a separable, projective Hilbert space (i.e. two states differing by an overall complex constant are equivalent). The kets e....
• 6,487