Lect13 - Lecture 13, p 1 But why must I treat the measuring...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture 13, p 1 But why must I treat the measuring device classically? What will happen to me if I d o n t ??--Eugene Wigner There is obviously no such limitation I can measure the energy and look at my watch; then I know both energy and time!--L. D. Landau, on the time-energy uncertainty principle When I hear of Schrdingers cat, I reach for my gun.--Stephen W. Hawking Lecture 13, p 2 Lab 3 Comments Lab 3 meets this week if you are normally in 132 Loomis. Lab 3 meets next week if you are normally in 164 Loomis. So does Discussion, and there is a quiz , so dont skip... For the lab: You will need your Active Directory Login See: http://www.ad.uiuc.edu You can save a lot of time by reading the lab ahead of time. Its a tutorial on how to draw wave functions Lecture 13, p 3 Lecture 13: Superposition & Time-Dependent Quantum States x | (x,t )| 2 U= U= x L | (x,t=0)| 2 U= U= x L Lecture 13, p 4 Last Week Time-independent Schrodingers Equation (SEQ): It describes a particle that has a definite energy, E . The solutions, (x), are time independent ( stationary states ). We considered two potentials, U(x): Finite-depth square well Boundary conditions. Particle can leak into forbidden region. Comparison with infinite-depth well. Harmonic oscillator Energy levels are equally spaced. A good approximation in many problems. ) ( ) ( ) ( ) ( 2 2 2 2 x E x x U dx x d m = +- Lecture 13, p 5 Today Time dependent SEQ: Superposition of states and particle motion Measurement in quantum physics Schrdingers cat Time-energy uncertainty principle Lecture 13, p 6 Time-Dependent SEQ To explore how particle wave functions evolve with time, which is useful for a number of applications as we shall see, we need to consider the time-dependent SEQ : Changes from the time independent version: E i d /dt We no longer assume a definite E. (x) (x,t) The solutions will have time dependence. i = (-1) appears The solutions will be complex. This equation describes the complete time and space dependence of a quantum particle in a potential U(x). It replaces the classical particle dynamics law, F=ma. The SEQ is linear in , and so the Superposition Principle applies : If 1 and 2 are solutions to the time-dependent SEQ, then so is any linear combination of 1 and 2 (example: = 0.6 1 + 0.8 i 2 ) 2 2 2 ( , ) ( , ) ( ) ( , ) 2 d x t d x t U x x t i m dx dt - + = Lecture 13, p 7 Review of Complex Numbers The equation, e i = cos + isin , might be new to you. It is a convenient way to represent complex numbers. It also (once you are used to it) makes trigonometry simpler....
View Full Document

This note was uploaded on 04/04/2011 for the course PHYSICS 214 taught by Professor Mestre during the Spring '11 term at University of Illinois at Urbana–Champaign.

Page1 / 31

Lect13 - Lecture 13, p 1 But why must I treat the measuring...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online