# What is the physical states in Heisenberg picture?

The physics states in Quantum mechanics is represented by vectors in Hilbert space, however in Heisenberg's picture, the equation of motion

$$\frac{d}{dt}A_H(t) = \frac{i}{\hbar}[H,A_H(t)]+\frac{\partial}{\partial t}A_H(t)$$

only deals with operators' time evolution.

I am confused that what is the physical state in Heisenberg picture?

• You may find this post useful physics.stackexchange.com/questions/173219/… – user929304 May 18 '16 at 12:13
• If you downvote this question, please at least tell me why. – Shing May 18 '16 at 14:59
• This paper describes the way reality works in terms of the Heisenberg picture arxiv.org/abs/quant-ph/0104033. The PDF may not render properly in Chrome, but it will work in a pdf viewer. – alanf Jun 13 '19 at 12:27

The physical states in the Heisenberg picture are frozen in time, and can be made to coincide with the Schrodinger-picture state at any given time $t_0$. In other words, $$|\psi(t_0)\rangle^S=|\psi\rangle^H$$ which doesn't evolve with time.