Solving of schrodinger's wave equation

In summary, the conversation is about applying the Schrodinger wave equation to the hydrogen atom and needing help with solving the first step. The equation is given in both Cartesian and polar coordinates, and the person is seeking an explanation of how to solve it in easy steps. They are advised to look for example derivations online and are assured that there are many resources available to help with the process.
  • #1
Chemer
27
0
It's the application of Shrodinger wave equation to H-atom and I can't solve the first step. Please help me solve this. I'm not maths student so it's really hard to solve it:(
d^2 psi/dx^2+d^2psi/dy^2+d^2psi/dz^2+8π^2m/h^2(E-V)=0

Where x= rsin(theta)cos(phi)
y=rsin(theta)sin(phi)
z=rcos(theta)
V=-e^2/r

When we convert Cartesian plans into polar planes, we get:

1/r^2 . d/dr(r^2.d(psi)/dr)+1/r^2sin(theta) . d/d(theta) (sin(theta).d(psi)/d(theta))+ 1/r^2sin^2(theta). d^2(psi)/d(phi)^2+8π^2m/h^2(E+e^2/r)(psi)=0
Please explain in easy steps, how to solve this?
 
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  • #2
Have you tried looking for example derivations online?
i.e.

We can help you with where you get stuck. There are many resources for showing you how to do this.
Basically it involves noticing that you can separate out the radial and angular components, then looking up the form of the resulting DEs (nobody does it from scratch).
 

1. What is Schrodinger's wave equation?

Schrodinger's wave equation is a fundamental equation in quantum mechanics that describes the time evolution of a quantum system. It was developed by the Austrian physicist Erwin Schrodinger in 1926.

2. Why is solving Schrodinger's wave equation important?

Solving Schrodinger's wave equation allows us to determine the wavefunction of a quantum system, which contains all the information about the system's position, momentum, and energy. This is crucial for understanding and predicting the behavior of particles on a quantum scale.

3. What are the key steps in solving Schrodinger's wave equation?

The key steps in solving Schrodinger's wave equation are: (1) writing the wave equation in its general form, (2) applying boundary conditions, (3) simplifying the equation using mathematical techniques, and (4) solving for the wavefunction.

4. Can Schrodinger's wave equation be solved for all quantum systems?

No, Schrodinger's wave equation is only applicable to non-relativistic systems and cannot be solved for systems with multiple particles or interactions. In these cases, other equations and methods must be used.

5. What are the practical applications of solving Schrodinger's wave equation?

Solving Schrodinger's wave equation has numerous practical applications, including predicting the energy levels and behavior of atoms and molecules, understanding the properties of materials, and developing new technologies such as quantum computers.

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