1. Shrödinger Equation

4. Time independent Schrödinger eqn.

5. Solution in constant potential

6. Eigenvalue equation
: Eigenfunction
: Eigenvalue

7. Hermitian operators have real eigenvalues
Eigenfunctions of momentum operator

8. Eigenfunctions of Hamiltonian H
Etc.

9. Etc.

10. If
Orthogonality
Normalisation

12. Assuming orthonormal eigenfunctions
Expectation or average value of energy
Probability of obtaining eigenvalue Ei

13. Example:
Normalised

14. Expectation value of an operator
for a state

15. Particle in a box of size L

17. 2 L L 2 L L

18. 2 L L 2 L L

19. Find the probability that a particle
trapped in one dimensional box of length
L can be found between 0.45L and 0.55L
for the ground state.

21. V -V One dimensional Potential well Infinite
~ same as particle in a box V L -V

22. Finite depth well
Finite V L -V

23. One dimensional Potential stepV V
E < V x

24. Quantum mechanical tunneling
One dimensional Potential barrier
Quantum mechanical tunneling
E < V V x

25. Quantum mechanical tunnelingV V x
More the barrier height less the transmission probability
More the barrier width less the transmission probability