A practice problem with Schrodinger equation

AI Thread Summary
The discussion centers on the application of the time-independent Schrödinger equation with a focus on the condition E=0. Participants clarify that setting E to zero simplifies the equation, leading to the right-hand side becoming zero. There is confusion regarding the presence of a constant term in the wave function for a simple harmonic oscillator, with an emphasis on the necessity of two terms in the second derivative of the wave function. Additionally, the concept of separating variables into spatial and temporal components is addressed, with advice to focus solely on the spatial part when dealing with the non-time-dependent equation. The conversation concludes with a sense of urgency as the original poster seeks to finalize their assignment.
drop_out_kid
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Homework Statement
In the comment section
Relevant Equations
Schrodinger equation
1649895929014.png


So my question is.. Is schrodinger equation for this problem like this?:
1649896912516.png


How to use the condition that E=0?

Thank you
 
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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.
 
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vela said:
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:
1649897690574.png


Could you take a look if it's right? I thought this is probably too trivial that xmin is just 0?
 
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?
 
vela said:
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!
 
##\psi''## should have two terms. Neither term disappears when you divide by ##\psi##.
 
vela said:
##\psi''## should have two terms. Neither term disappears when you divide by ##\psi##.
Thank you so much... I am doing it again
 
vela said:
##\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
 
drop_out_kid said:
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 Schrodinger ///non-time-dependent/// equation (the one you posted (missing an E of energy) at the first post) you should not worry with time.
 
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LCSphysicist said:
I have no idea of what is a sai(t). But if you are solving the Schrodinger ///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 !
 
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