**UFBA**

# Physics of high technology devices

(Parte **1** de 3)

PHYS1180 -Physics of High Technology Devices

Lecture 24 –The Quantum & Nano-worlds: Quantum confinement and resonators

Dr. Geoff Pryde Room 1.12 Physics Annex 3365 1026 pryde@physics.uq.edu.au

Key points & learning objectives

1.What is quantum confinement?

2.How does confinement affect the energy level structure?

3.What are quantum harmonic oscillators and how do they interact with the environment?

Physics –quantum physics

Review: the Bohr model –stable orbits

?Bohr postulated that conventional EM theory did not apply on the atomic scale –a different Physics was needed!

?He constructed a theory in which the electrons were confined to a series of stable orbits of fixed radii (and hence energy and orbital angular mo mentum).

?Radiation is emitted (or absorbed) in “quanta”when electrons make transitions between these fixed states.

?Theory successfully predicted the hydrogen spectra.

n=1 n=2 n=3 ke E n=1 (ground state) n>1 (excited state) n=infinity (ionised)

Review: Quantisation of orbital angular momentum

“The quantisation of angular momentum is a postulate un-derivable from any deeper laws. It’s validity depends simply upon the agreement of the Bohr model with experiment”.

?i.e. Bohr had no real physical reason for stating that the orbits were fixed, and that the electrons would have fixed angular momenta and energies

?Another problem –why should electrons of different initial energies all “collapse”into the same set of fixed energies?

Summary & conclusions -last lecture

1.Quantum physics is needed to describe the behaviour of nano-scale devices

2.Quantum physics is a probabilistic science, and correctly predicts / explains atomic structure and the behaviour of tiny particles

3.Particles can behave like waves, and their behaviours are described by the associated wavefunctions and quantum numbers

4.Schrodingers wave equation is a pivotal theory in quantum physics, and can be used to predict the wavefunction at any subsequent time if some initial conditions are known

5.Classical physics is just a limiting form of quantum physics where the number of particles is very large

6.Quantum physics will be at the heart of many new high technology innovations

Lecture Outline

?Key points & learning objectives

?Time independent Schrödinger equation ?Confinement: particle in an infinite square well

?Real life quantum confinement

?The quantum harmonic oscillator

? Nanom echanical resonators

?Summary & conclusions

SE –Time Independent Form

?If U(x)is truly only spatially dependent (for example for standing wave problems), then separation of variables is often used to solve SE:

?SE can be reduced to the time independent formwhich is useful for predicting lots of systems ( E =energy):

?What are the analogies to the classical wave equation?

?Schrödinger used this approach to solve: ?Particle in 1D box

?Harmonic oscillator

?1D Hydrogen atom

Particle in a Box (Infinite Square Well)

?Classical analogy: a ball bouncing elastically off the inside walls of a box

?The ball does not leave the confines of the box, because it does not have enough energy

?More general analogy: a charged particle confined within a potential well which has infinite potential at its walls

?The charged particle can never escape from the confines of the potential well –it has zero probability of being found outside the well

?Its wavefunction in the regions of space x<0, x>L is ZERO

?For 0<x<L, what do we expect classically?

U(x)

U=0 x=Lx=0

Finding Ψ(x) Inside the Box

?1-D time independent problem where U(x)=0inside the box and U(x)=∞at x=0 and x=L

(Parte **1** de 3)