# Role of hermitian and unitary operators in QM

1. Jul 23, 2012

### Inam

Which is the role of hermitian and unitary operators in quantum mechanics and which operator is neither hermitian nor unitary

2. Jul 23, 2012

### tom.stoer

Observables must be hermitian operators b/c we associate experimental measurable values with eigenvalues, therefore eigenvalues must be real - which is ensured by hermitian operators.

For every hermitian operator O you can construct a family of unitary operators U(s) = exp(iOs) with a real parameter s. These U(s) may be symmetries which act on Hilbert space states as unitary operators. One example is a hermitian angular momentum operator Li which generates rotations w.r.t. to the i-axis. A special case are time translations which are generated by the hermitian Hamiltonian H, i.e. U(t) = exp(iHt).

Important operators which are neither hermitian nor unitary are a) the creation and annihilation operators of the harmonic oscillator and b) the ladder operators for angular momentum.

3. Jul 23, 2012

Thanks Tom