Heisenberg's & Schrodinger's Picture

  • Thread starter Eynstone
  • Start date
  • #1
336
0

Main Question or Discussion Point

Is the Heisenberg's picture really equivalent to Schrodinger's ?
It may seem so at a first glance & both produce the same results.But space & time are treated equally in Heisenberg's formulation : the operators are time dependent.In Schrodinger's formulation, states are time-dependent while the hamiltonian may be time-independent. This makes the former congruous & adaptable to relativity.
Also, the initial state vector remains fixed & operators move in Heisenberg's formulation. The initial state is not of so great a consequence as in Schrodinger's picture. Hence, it is more congruous with quantum field theory .(When particle creation & annihilation is involved, we can't work with a state vector in a Hilbert space).
I wonder how the two become totally compatible in the non-relativistic formulation.
 

Answers and Replies

  • #2
DrClaude
Mentor
7,269
3,424
It is easy to show mathematically that the two pictures give equal results.

A simple ways to visualize it is to consider that the Schrödinger picture corresponds to a lab-fixed reference frame, in which the state of the quantum system will evolve, while the Heisenberg picture corresponds to a system-fixed reference frame, where the state remains unchanged but the world around (including measuring apparatuses) move as a function of time.
 

Related Threads on Heisenberg's & Schrodinger's Picture

  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
3
Views
5K
  • Last Post
Replies
4
Views
8K
Replies
10
Views
720
Replies
2
Views
863
Replies
4
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
9
Views
3K
  • Last Post
Replies
3
Views
946
  • Last Post
Replies
11
Views
5K
Top