Serious conceptual problem with QM (eigenfunctions)

In summary, it is generally advised to assume that the potential is not time-dependent when working with eigenfunctions of different observables. This is because the TISE equation only applies for time-independent potentials.
  • #1
sachi
75
1
The wavefunction psi is often separated into two parts, the time dependent part and the part which has only spatial dependence (phi), and this I think can only be done if we assume that the potential is not a function of time. I often see proofs where we have H acting on phi (not psi) and we get H (phi1) = E1*phi1. However this equation is essentially just the TISE, which of course only applies for time independent potentials. Does this mean that we should generally assume that the potential is not a function of time while working with eigenfunctions of different observables?

Also, does the potential not being a function of time essentially the same as having an isolated system?

Sachi
 
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  • #2
time indep.: No, not in general. Time-dependent perturbation theory is the first counterexample I thought of.
 
  • #3
sachi said:
The wavefunction psi is often separated into two parts, the time dependent part and the part which has only spatial dependence (phi), and this I think can only be done if we assume that the potential is not a function of time.

If the Hamiltonian is explicitely time independent, we can factorize the time-dependence of the state vactor into an exponential containing the spectral values of the Hamiltonian.

Sachi said:
I often see proofs where we have H acting on phi (not psi) and we get H (phi1) = E1*phi1. However this equation is essentially just the TISE, which of course only applies for time independent potentials. Does this mean that we should generally assume that the potential is not a function of time while working with eigenfunctions of different observables?
Also, does the potential not being a function of time essentially the same as having an isolated system?
Sachi

Isolated systems involve (at classical level) the absence of external force fields. The only possible interactions are the internal ones which are generally time independent...

Daniel.
 

1. What is the serious conceptual problem with QM eigenfunctions?

The serious conceptual problem with QM eigenfunctions is that they do not provide a complete description of a physical system. While they can accurately predict the values of observable properties such as energy and momentum, they do not fully explain the behavior and interactions of particles.

2. How does this problem arise in quantum mechanics?

This problem arises in quantum mechanics because the theory is based on the assumption that particles can exist in multiple states simultaneously, known as superposition. However, this conflicts with our everyday experience and understanding of the physical world.

3. Can this problem be solved?

There is ongoing debate among scientists about whether this problem can be solved. Some argue that it is a fundamental limitation of the theory, while others propose alternative interpretations or modifications of quantum mechanics to address this issue.

4. How does this problem impact our understanding of the universe?

The serious conceptual problem with QM eigenfunctions has significant implications for our understanding of the universe. It challenges our notions of reality and raises questions about the nature of particles and their interactions. It also has implications for the development of future technologies, such as quantum computing.

5. What are some proposed solutions to this problem?

Some proposed solutions include the many-worlds interpretation, which suggests that all possible outcomes of a measurement exist in parallel universes, and the pilot wave theory, which posits the existence of an underlying wave that guides the behavior of particles. Other solutions involve modifying the mathematical framework of quantum mechanics, such as the Bohmian mechanics approach.

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