# Uncertainity relation

1. Oct 7, 2008

### yukawa

Show that [A,B] = AB - BA = iqI, where q is a real no. and I is the identity matrix, cannot be satisfied by any finite dimensional Hermitian matrix A and B.

I think this problem is something related to the uncertainity relation:
$$<(\Delta A)^{2}><(\Delta B)^{2}>\geq \frac{\left|C\right| ^{2}}{4}$$
but I don't know how to find the variance of A and B .......

How should I approch this problem? Are there any trick to do with the "finite dimension" ?

2. Oct 8, 2008

### borgwal

No, the problem has nothing to do with the uncertainty relations. Try taking the trace of both left-hand and right-hand sides of your equation.