How can I use Mathematica to solve the 1-D,time independent Schrodinger Equation and verify the Bohr's radius? - mathematica 5.2 for mac rar
I) with Mathematica 5.2 to solve the 1-D to time-independent equation Schodinger (wave function. How can the Bohr radius for hydrogen atom ground state?
Saturday, January 23, 2010
Mathematica 5.2 For Mac Rar How Can I Use Mathematica To Solve The 1-D,time Independent Schrodinger Equation And Verify The Bohr's Radius?
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If you are the separation of variables in the Schrodinger equation used in 3D, derived from the radial equation, the 1D-differential equation for the radial wave function of the hydrogen atom.
This equation is presented here:
http://galileo.phys.virginia.edu/classes/751.mf1i.fall02/HydrogenAtom_files/image057.gif
You can use the Mathematica dsolve in the differential equation. When Mathematica cause problems (the solutions are somewhat complicated, but easily accessible online), just put l = 0 You can do this because I really want to find only in the ground state Bohr radius.
Once Mathematica has radial wave functions for l = 0, want the solution of the eigenvalue problem to choose the lowest energy (ground state) to. Find the expected value of r (\\ \\ \\ \\ \\ \\ \\ \\ u0026lt, u0026lt r> = \\ \\ \\ \\ \\ \\ \\ \\, u (r) | r | u (r)) on the radial or shaft fucntion (R), and you should now see the classical Bohr radius.
If you are the separation of variables in the Schrodinger equation used in 3D, derived from the radial equation, the 1D-differential equation for the radial wave function of the hydrogen atom.
This equation is presented here:
http://galileo.phys.virginia.edu/classes/751.mf1i.fall02/HydrogenAtom_files/image057.gif
You can use the Mathematica dsolve in the differential equation. When Mathematica cause problems (the solutions are somewhat complicated, but easily accessible online), just put l = 0 You can do this because I really want to find only in the ground state Bohr radius.
Once Mathematica has radial wave functions for l = 0, want the solution of the eigenvalue problem to choose the lowest energy (ground state) to. Find the expected value of r (\\ \\ \\ \\ \\ \\ \\ \\ u0026lt, u0026lt r> = \\ \\ \\ \\ \\ \\ \\ \\, u (r) | r | u (r)) on the radial or shaft fucntion (R), and you should now see the classical Bohr radius.
If you are the separation of variables in the Schrodinger equation used in 3D, derived from the radial equation, the 1D-differential equation for the radial wave function of the hydrogen atom.
This equation is presented here:
http://galileo.phys.virginia.edu/classes/751.mf1i.fall02/HydrogenAtom_files/image057.gif
You can use the Mathematica dsolve in the differential equation. When Mathematica cause problems (the solutions are somewhat complicated, but easily accessible online), just put l = 0 You can do this because I really want to find only in the ground state Bohr radius.
Once Mathematica has radial wave functions for l = 0, want the solution of the eigenvalue problem to choose the lowest energy (ground state) to. Find the expected value of r (\\ \\ \\ \\ \\ \\ \\ \\ u0026lt, u0026lt r> = \\ \\ \\ \\ \\ \\ \\ \\, u (r) | r | u (r)) on the radial or shaft fucntion (R), and you should now see the classical Bohr radius.
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