Schrodinger's Equation in terms of vacuum permittivity?

In summary, the conversation discusses Schrodinger's Equation and its use in a particular problem. The equation is stated to be the time-independent Schrodinger Equation and includes the potential term e^2/r, which represents the Coulomb potential due to the nucleus. The individual was seeking clarification on the equation and its application in the problem.
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Summary:: How can Schrodinger's Equation be written relative to vacuum permittivity

I am wondering why a particular problem uses this equation:
ss01.png

It is stated to be Schrodinger's equation. Where does the potential come in, as well as the e^2/r ?
An explanation would be greatly appreciated. Thanks.
 
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currently said:
a particular problem

What problem? Please give a reference.
 
  • #3
PeterDonis said:
What problem? Please give a reference.
Here's the problem. the equation was stated in class to be Schrodinger's Equation.
Last problem should say: n, l, and m are arbitrary constants.

ssfull.png
 
  • #4
currently said:
the equation was stated in class to be Schrodinger's Equation

It is. More precisely, it's the time-independent Schrodinger Equation, i.e., it's the eigenvalue equation that stationary states have to satisfy.

currently said:
Where does the potential come in, as well as the e^2/r ?

The ##e^2 / r## term is the potential; it's the Coulomb potential due to the nucleus, in SI units.
 
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PeterDonis said:
It is. More precisely, it's the time-independent Schrodinger Equation, i.e., it's the eigenvalue equation that stationary states have to satisfy.
The ##e^2 / r## term is the potential; it's the Coulomb potential due to the nucleus, in SI units.
Ok, thank you. I wanted to make sure it was the correct equation.
 

1. What is Schrodinger's Equation in terms of vacuum permittivity?

Schrodinger's Equation in terms of vacuum permittivity is a fundamental equation in quantum mechanics that describes how the wave function of a physical system changes over time. It takes into account the vacuum permittivity, which is a measure of the ability of a vacuum to support an electric field.

2. How is vacuum permittivity related to Schrodinger's Equation?

Vacuum permittivity is a crucial component in Schrodinger's Equation because it represents the electric field that particles experience in a vacuum. This allows the equation to accurately describe the behavior of particles at the quantum level.

3. Can Schrodinger's Equation be solved without considering vacuum permittivity?

No, Schrodinger's Equation cannot be solved without considering vacuum permittivity. This is because the equation is based on the fundamental principles of quantum mechanics, and vacuum permittivity is an essential part of those principles.

4. How does vacuum permittivity affect the behavior of particles in Schrodinger's Equation?

Vacuum permittivity plays a crucial role in determining the energy levels and behavior of particles in Schrodinger's Equation. It affects the strength of the electric field that particles experience, which in turn affects their motion and interactions with other particles.

5. Why is it important to consider vacuum permittivity in Schrodinger's Equation?

Considering vacuum permittivity in Schrodinger's Equation is important because it allows for a more accurate and comprehensive understanding of the behavior of particles at the quantum level. Without it, the equation would not be able to accurately describe the behavior of particles in a vacuum.

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