Overview
De Broglie–Bohm theory is based on the following:
We have a configuration of the universe, described by coordinates, which is an element of the configuration space . The configuration space is different for different versions of pilot wave theory. For example, this may be the space of positions of particles, or, in case of field theory, the space of field configurations . The configuration evolves (for spin=0) according to the guiding equation
- .
Here, is the standard complex-valued wavefunction known from quantum theory, which evolves according to Schrödinger's equation
This already completes the specification of the theory for any quantum theory with Hamilton operator of type .
If the configuration is distributed according to at some moment of time, this holds for all times. Such a state is named quantum equilibrium. In quantum equilibrium, this theory will agree with the results of standard quantum mechanics.
Read more about this topic: Bohmian