Can I Tell if a State is Ground State?

[KFC]

If I know the explicit form of potential, the energy and a specific eigenstate, but I don't know the general form of eigenstates and eigenvalues, can I tell if the state is ground state or not?

 

[malawi_glenn]

No i don't think so, why are you asking?

 

[Meir Achuz]

If I know the explicit form of potential, the energy and a specific eigenstate, but I don't know the general form of eigenstates and eigenvalues, can I tell if the state is ground state or not?

A ground state wave function usually has no nodes.

 

[tim_lou]

A ground state wave function usually has no nodes.

I think you can prove this statement by noting that the ground state wave function minimizes
$$\left < \psi \right| H \left | \psi \right>$$

 

[intervoxel]

The Variational Principle guarantees that

$$E_g \leq \langle \psi|H|\psi \rangle \equiv \langle H \rangle$$

 

[msumm21]

In doing some QM problems a few weeks ago I noticed that, for the PARTICULAR potential I was working with, the product of the standard deviation of the position (sx) and the standard deviation of the momentum (sp) was exactly hbar/2 in the ground state (sx*sp=hbar/2), and the product grew larger for higher energy states. So the uncertaintly principle was closest to getting violated in the lowest energy state. I assume that's NOT true for other potentials, but maybe something you could look into depending upon what exactly you are trying to do.