Flowchart for Solving Schrodinger START HERE Are you solving a problem rela:ng to quantum mechanical par:cle mo:on? If Spherical (and a central poten:al), you have a lookup chart for Y, the wave func:on (aka spherical harmonics) of theta and phi, based on the l and m_l values. You don’t need to solve for this. Write down the posi:on only Schrodinger eqn (for x or r) Use a Schrodinger Equa:on! Is it a Cartesian or Spherical coordinate problem? (hint, look at the form of the poten:al, V) If solving for x, rearrange equa:on so that you have only the second deriva:ve on the leM side, and some stuff :mes the wavefunc:on on the right side. If solving for r, can use a lookup table to find R(r) for a given n and l value. The E has a very specific form for a central poten:al, you can just write that down You can choose to solve the differen:al radial Sch. eqn, that’s a bit of work but not too hard. I don’t recommend doing this on an exam Flowchart for Solving Schrodinger If solving for x, rearrange equa:on so that you have only the second deriva:ve on the leM side, and some stuff :mes the wavefunc:on on the right side. If solving for r, can use a lookup table to find R(r) for a given n and l value. The E has a very specific form for a central poten:al, you can just write that down You can choose to solve the differen:al radial Sch. eqn, that’s a bit of work but not too hard. I don’t recommend doing this on an exam There are very characteris:c solu:ons to the Cartesian coordinate Schrodinger equa:on, based on what your Ψ’’ = stuff * Ψ equa:on looks like. Write the solu:on down. Apply boundary condi:ons to solve for variables in your wavefunc:ons. Boundary condi:ons will also produce quan:zed equa:ons for E, etc. Normalize your wavefunc:on to find the normaliza:on constants If you only need values for the E levels, you can stop here! Go to next page! Flowchart for Solving Schrodinger Apply boundary condi:ons to solve for variables in your wavefunc:ons. Boundary condi:ons will also produce quan:zed equa:ons for E, etc. Normalize your wavefunc:on to find the normaliza:on constants Is it :me independent or :me dependent? If :me independent you’re done! If :me dependent, mul:ply the :me independent part by the :me independent solu:on If you only need values for the E levels, you can stop here, no need to normalize! Now you need to actually apply the condi:ons of the problem (ie, the n, l, m_l, x, r, values that are appropriate) to reduce the solu:on, or to find the probability density, E values, etc.