A practice problem with Schrodinger equation

  • #1
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
 

Answers and Replies

  • #2
vela
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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.
 
  • #3
drop_out_kid
34
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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.
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?
 
  • #4
vela
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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?
 
  • #5
drop_out_kid
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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!
 
  • #6
vela
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##\psi''## should have two terms. Neither term disappears when you divide by ##\psi##.
 
  • #7
drop_out_kid
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##\psi''## should have two terms. Neither term disappears when you divide by ##\psi##.
Thank you so much... I am doing it again
 
  • #8
drop_out_kid
34
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##\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
 
  • #9
LCSphysicist
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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.
 
  • #10
drop_out_kid
34
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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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