Physical interpretations of Schrodingers equation

[Quantum_man]

1. Hi all, I am doing a practice exam attempt and I am stuck on this question:

What is the physical interpretation of |ψ(r,t)| and |ψ(r,t)|^2? Can the wavefunction
|ψ(r,t)| be measured directly?



My attempt was:

The Schrödinger equation describes the relationship between the energy and momentum of a particle. Wavefunction squared explains the probability of finding a particle in a given region. And the wave function can't be measured directly.

Any help would be appreciated, thanks.

 

[PhysicsGente]

This is Shcodinger's eq. i\hbar\frac{\partial\psi}{\partial t}=H\psi. Now, look at the variables and tell me what it describes (although it seems that you are not been asked this).

You need to think about probabilities to answer the first part. As for the second question, I really don't know what it means to measure SE "directly".

 

[Quantum_man]

Its describing energy of a particle with respect to time. Thats what it seems like.

 

[Fightfish]

Wavefunction squared explains the probability of finding a particle in a given region.

To be precise, $|\psi (r,t)|^{2} dV$ gives the probability of finding the particle in a small region $dV$ about the point $r$

Its describing energy of a particle with respect to time. Thats what it seems like.

Unless you have a dissipative Hamiltonian, the energy of the system is conserved. (in fact dissipative / open systems cannot be properly described using the Schrödinger equation)

 

[Quantum_man]

Hi Thanks for replying FightFish, can you give me an example of a dissipative system?

 

[Fightfish]

A damped quantum harmonic oscillator. Physically that might correspond to say inter-molecular bonds. Other systems include light-atom interactions, where there might be emission / absorption processes.