Word File Edit View Insert Format Tools Table Window Help G 97% . Q Wed Apr 24 10:37 AM AutoSave O A A . CGP ... w- final-exam-2024s Q Search (Cmd + Ctrl + U) Home Insert Draw Design Layout References Mailings Review View Comments Editing Share Calibri (Bo... v 11 ~ A A Aav Ap EVEEVEE T AaBbCcDdEe AaBbCcDdEe AaBbCCD AaBbCcDdE Paste BIUvab X X A DAY Normal No Spacing Heading 1 Heading 2 Styles Dictate Sensitivity Add-ins Editor Pane 2. In lecture we discussed the 2-D particle in a box model. The model applies to any QM particle in a rectangular planar confining potential (electron, neutron, alpha particle etc.). Now consider a system where we have added to our 2-D PIB setup not one but three non-interacting QM particles 2.2 Can the separation of variables method be used to solve the Schrodinger equation for the above system? If yes, explain. If no, also explain your reasoning. 2.3 Write down the complete wavefunction describing the state of the three particles. 4(x1. V1,X2, y2, X3, y3 )= where ri = (x1, y1) represents the position of particle 1 and r2 = (X2, y2) is the position of particle 2 and 13 = (X3, )3) is the position of particle 3. (Hint: How many independent quantum numbers need to be included in the above equation for the wavefunction?) 2.4 What is the normalization coefficient for the wavefunction P(x1, y1.X2, V2,X3, )3)? [5 points] N= 2.5 Is the above model for the wavefunction 4 (X1, V1, X2, V2, X3, 13) (3 independent particles in a 2-D box) applicable to: Explain your reasoning in each case Three alpha particles in a rectangular 2-D potential? Three neutrons in a square potential? 99+ O Three valence electrons in the porphine molecule? 2 Porphine (free base form) Page 1 of 3 331 words X English (United States) & Accessibility: Investigate Focus E + 119% APR 24 4 W G