A practice problem with Schrodinger equation

[drop_out_kid]

Homework Statement

In the comment section

Relevant Equations

Schrodinger equation

So my question is.. Is Schrödinger equation for this problem like this?:

How to use the condition that E=0?

Thank you

 

[vela]

The time-independent Schrödinger equation is
$$-\frac{\hbar^2}{2m}\psi''(x) + V(x)\psi(x) = E\psi(x).$$ When you set $E=0$, the righthand side becomes 0.

 

[drop_out_kid]

The time-independent Schrödinger equation is
$$-\frac{\hbar^2}{2m}\psi''(x) + V(x)\psi(x) = E\psi(x).$$ When you set $E=0$, the righthand side becomes 0.

Exactly. And I solve it as this:

Could you take a look if it's right? I thought this is probably too trivial that xmin is just 0?

 

[vela]

I'd expect there should be a constant term as well.

The given wave function is one of the energy eigenstates for the simple harmonic oscillator. What's the potential energy function for the simple harmonic oscillator?

 

[drop_out_kid]

I'd expect there should be a constant term as well.

The given wave function is one of the energy eigenstates for the simple harmonic oscillator. What's the potential energy function for the simple harmonic oscillator?

-1/2kx^2?

So where is the constant come from ?? the phi(x) got cancelled..

Thank you so much for answering my question!

 

[vela]

$\psi''$ should have two terms. Neither term disappears when you divide by $\psi$.

 

[drop_out_kid]

$\psi''$ should have two terms. Neither term disappears when you divide by $\psi$.

Thank you so much... I am doing it again

 

[drop_out_kid]

$\psi''$ should have two terms. Neither term disappears when you divide by $\psi$.

So yes there's a constant! And I got another question: should I time a sai(t)? I am not familiar with it but I saw that phi(x,t) usually written to phi(x)*sai(t) and sai(t) is usually an exponential

 

[LCSphysicist]

So yes there's a constant! And I got another question: should I time a sai(t)? I am not familiar with it but I saw that phi(x,t) usually written to phi(x)*sai(t) and sai(t) is usually an exponential

I have no idea of what is a sai(t). But if you are solving the Schrödinger ///non-time-dependent/// equation (the one you posted (missing an E of energy) at the first post) you should not worry with time.

 

[drop_out_kid]

I have no idea of what is a sai(t). But if you are solving the Schrödinger ///non-time-dependent/// equation (the one you posted (missing an E of energy) at the first post) you should not worry with time.

Yes I think so. Now I got last problem of my assignment and last hour of due, thank you !