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Schrodinger equation

Schrodinger equation

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) The time evolution of a quantum system can be expressed in the differential form as follows Ə ih (r, t) = HV(r, t) Ət where H is the Hamiltonian operator H = ħ² d² 2m dx² i. Write down the condition under which the above equation holds ii. Express the above equation in 3 dimensional form. iii. Using separation of variables solve the time dependent Schrodinger equation and show that yn(r, t) = n(r)e-Ent and HVn (r) = Enn
Transcribed Image Text:(a) The time evolution of a quantum system can be expressed in the differential form as follows Ə ih (r, t) = HV(r, t) Ət where H is the Hamiltonian operator H = ħ² d² 2m dx² i. Write down the condition under which the above equation holds ii. Express the above equation in 3 dimensional form. iii. Using separation of variables solve the time dependent Schrodinger equation and show that yn(r, t) = n(r)e-Ent and HVn (r) = Enn
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