{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Lect15 - Lecture 15 Time-Dependent QM Tunneling Review and...

This preview shows pages 1–6. Sign up to view the full content.

Lecture 15, p.1 Lecture 15: Time-Dependent QM & Tunneling Review and Examples, Ammonia Maser 0 L U 0 x U(x) E x | ψ (x,t 0 )| 2 U= U= 0 x L | ψ (x,t=0)| 2 U= U= 0 x L

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Lecture 15, p 2 Measurements of Energy What happens when we measure the energy of a particle whose wave function is a superposition of more than one energy state? If the wave function is in an energy eigenstate (E 1 , say), then we know with certainty that we will obtain E 1 (unless the apparatus is broken) . If the wave function is a superposition ( ψ = a ψ 1 +b ψ 2 ) of energies E 1 and E 2 , then we aren’t certain what the result will be. However: We know with certainty that we will only obtain E 1 or E 2 !! To be specific, we will never obtain (E 1 +E 2 )/2 , or any other value. What about a and b? |a| 2 and |b| 2 are the probabilities of obtaining E 1 and E 2 , respectively. That’s why we normalize the wave function to make |a| 2 + |b| 2 =1 .
Lecture 15, p.3 Example An electron in an infinite square well of width L = 0.5 nm is (at t=0) described by the following wave function: Determine the time it takes for the particle to move to the right side of the well. 2 2 ( , 0) sin sin x t A x x L L L π π Ψ = = + | Ψ (x,t)| 2 U= U= 0 x L | Ψ (x,0)| 2 U= U= 0 x L

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Lecture 15, p.4
Lecture 15, p.5 ACT 1 An electron in an infinite square well of width L = 0.5 nm is (at t=0) described by the following wave function: 2 2 ( , 0) sin sin x t A x x L L L π π Ψ = = + 1 ) Suppose we measure the energy.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}