Could we do QM without time evolution ?

[mhill]

could we do QM without time evolution ??

that is the idea, could we perform QM without referring to any coordinate called 'time' in the sense that the Hamiltonian and Schroedinguer equation would be

$$H \Psi (x) =0$$ and time and energy only appear as the pair

$$(p_0 , t)$$

the idea is , to perform a QM where there is no time evolution

 

[strangerep]

that is the idea, could we perform QM without referring to any coordinate called 'time' in the sense that the Hamiltonian and Schroedinguer equation would be

$$H \Psi (x) =0$$ and time and energy only appear as the pair

$$(p_0 , t)$$

the idea is , to perform a QM where there is no time evolution

If you mean perform some kind of generally-covariant quantization in a
generalized phase space, I think Henneaux & Teitelboim talk about some
of that in their textbook. One finds weird stuff such as zero Hamiltonians,
(iirc - my memory is a bit vague on the details).

Separately, there's also the old chestnut about how time in QM is a
parameter, not an operator, if we want to have a Hilbert space of
states containing a lowest-energy state.