A practice problem with Schrodinger equation

In summary, the conditions that E=0 are necessary in order to solve the time-independent Schrödinger equation.
  • #1
drop_out_kid
34
2
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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  • #2
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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  • #3
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?
 
  • #4
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
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!
 
  • #6
##\psi''## should have two terms. Neither term disappears when you divide by ##\psi##.
 
  • #7
vela said:
##\psi''## should have two terms. Neither term disappears when you divide by ##\psi##.
Thank you so much... I am doing it again
 
  • #8
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
 
  • #9
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.
 
  • #10
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 !
 

What is the Schrodinger equation?

The Schrodinger equation is a mathematical equation that describes the behavior of quantum particles, such as electrons, in a given system. It takes into account the wave-like nature of particles and is used to determine the probability of finding a particle in a particular state.

How is the Schrodinger equation used in science?

The Schrodinger equation is used in many areas of science, including quantum mechanics, chemistry, and materials science. It is used to calculate the energy levels and wave functions of particles, which can then be used to make predictions about their behavior in different systems.

What is a practice problem with the Schrodinger equation?

A practice problem with the Schrodinger equation could involve solving for the wave function and energy levels of a particle in a given potential well. This could include calculating the probability of finding the particle at different points in the well and determining its average energy.

What are some real-life applications of the Schrodinger equation?

The Schrodinger equation has many real-life applications, such as in the development of new materials, understanding the behavior of atoms and molecules, and in the design of electronic devices. It is also used in medical imaging techniques, such as MRI, to study the behavior of particles in the body.

Is the Schrodinger equation difficult to understand?

The Schrodinger equation can be challenging to understand, as it involves complex mathematical concepts and deals with the behavior of particles at the quantum level. However, with proper study and practice, it can be understood and applied to various scientific problems.

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