3. Schrodinger Equations

Question 1

Briefly describe how the schrodinger equation is formed

Answer 1

• Start off with the TDSE which states the kinetic + potential energies are equal to the total energy of a system
• Transform the momentum to its quantum counterpart

Question 2

Describe how the TISE is formed

Answer 2

• Start off with the TDSE and assume the potential is only a function of position rather than position and time ( V(r) not V(r,t)
• Separate variables from Ψ(r,t) = u(r)f(t) and sub in, then divide by them

Question 3

What is the TISE?

Answer 3

An energy eigenvalue equation

Also describes the wavefunctions

Question 4

What is the TDSE?

Answer 4

An equation of motion

Question 5

What do you substitute in as a solution when solving the TDSE?

Answer 5

f(t) = A exp(-iwt)

Question 6

Graphically what does the TDSE show?

Answer 6

As time progresses, f(t) rotates around a unit circle with phase factor in Ψ, with wt as its angle on a complex graph

Question 7

What is a stationary state?

Answer 7

A quantum state with all observables independent of time

Question 8

Mathematically, how can the stationary state be shown?

Answer 8

Ψ(r,t) | ^2 does not change in time

Question 9

When do stationary states apply?

Answer 9

• When the potential does not depend on time

- When the system evolves without us making any measurements on it

Question 10

What happens when we measure a quantum system?

Answer 10

It abruptly jumps to one of its eigen states