Introduction to Quantum Physics

Early Atomic Physics

What is Quantum Physics

Quantum Physics is a collection of laws which explain observations of the tiny building blocks of all matter.

The world of the quantum must be able to explain the classical world that we live in.

To understand the quantum world we need to understand one of the major building blocks ---- the atom

History of Atomic Structure

The model of atomic structure has changed as observations have altered our perceptions Democrictus Dalton Thomson Rutherford ………. (The model is not complete)

Democritus

Atoms (Greek for indivisible) are the smallest unit of matter

Atoms share all of the properties of the macroscopic object

Atoms are the smallest pieces of matter which still act as the material from which they come from

John Dalton

First truly scientific theory of the atom (results discovered through experiments with marsh gases)

Proof of early Greek model --- the atom is indivisible but with no internal structure

Properties of matter come

from the properties of the atom

But what about electricity?

J.J. Thomson

Discoverer of the electron

The atom consists of a positively charged substance (like pudding) containing negative charges (like the raisins in a plum pudding)

Rutherford

1909 – Rutherford performs an experiment in which alpha particles (He nucleus) are fired towards a thin foil of gold

Rutherford

Experimental observations indicated that the majority of the alpha particles passed straight through, with few being deflected at small angles and even fewer retro reflecting from the gold foil

Rutherford

Observations indicate that the atom is mostly empty space with a dense, central, positively-charged structure at its center

The electrons (discovered by Thomson) must therefore exist outside of this central nucleus …. Orbiting around the nucleus as planets do the Sun.

Classical Model

The Rutherford model of the atom became known as the classical model of the atom

Problem with the classical Model

The Theory The electron has a negative charge and orbits about

the central nucleus The central nucleus has a charge and therefore must

also have a magnetic field Charged particles lose energy as they pass through a

magnetic field

According to classical electro-magnetic theory the electron should lose energy in its orbit.

Observations The atom is a stable structure consisting of

sub atomic particles that do not normally decay in our life time.

Because the observation does not match the theory …. either classical physics is wrong OR the Rutherford model is wrong / incomplete

Which is easier to believe ? Hundreds of years of Physics laws and

theories are wrong. A relatively new model of our atom is wrong.

Answer : Both classical physics and the Rutherford

model have some minor problems.

Enter Niels Bohr

Bohr succeeded in solving the problem with the classical model by uniting two disparate ideas : Planck’s quanta and the hydrogen emission spectra

Max Planck

Observed the temperatures of cannons as they were bored out

The colour of the emitted

radiation is related to the

temperature of the cannon

The expected peak intensity follow the Rayleigh-Jean

law

Rayleigh-Jean Law

Ultraviolet Catastrophe

The classical (Rayleigh-Jeans) model predicted a steady increase in Intensity well into the ultraviolet

If the theory worked with

the cannons then enough

ultraviolet radiation would

be emitted to destroy life.

Energy is not continuous

Planck solved the “catastrophe” by re-imagining Energy

Energy is not a continuous stream but consists of chunks or discrete packets

Energy is quantized (flows as quanta)

Planck did not initially believe in his findings Why would energy be quantized … it is

neither simple or beautiful

Planck’s findings were instrumental in the work for which Einstein won the Noble Prize in Physics Photoelectric Effect

Quanta of Energy

Vibrating molecules can only vibrate with certain discrete amounts of energy

Each quanta of energy can be determined by E = hf E is the energy of the Quanta (J or eV) f is the frequency of the vibration h is Planck’s constant (6.626 x 10-34 Js)

Hydrogen emission spectra

Bohr also received a clue from the emission spectra of the Hydrogen atom

Again the classical model predicts that the atom should be able to radiate in an infinite range of wavelengths but observations indicate otherwise

Energy is quantized

If the electron in the atom can only absorb or emit discrete quantities of energy (quanta) then the emission spectra makes senseBy using Planck’s hypothesis and the clues from the emission spectra of Hydrogen Bohr was able to mathematically explain the nature of the atom

Hydrogen emission spectra

Bohr’s theory

Bohr’s theory was the first step in the Quantum revolution

Postulate of Stationary States : the Hydrogen atom can exist, without radiating energy, in any one of a discrete set of orbits of fixed energy

Frequency Postulate : the Hydrogen atom can emit or absorb a quantity of energy only when the electron changes from one stationary state into another. This amount can be calculated by E=hf

Question

How does the concept of the quantization of energy circumvent the problem with the classical model?

The Atom so far ….

A central nucleus (of positive charge) is surrounded by negatively charged particles called electrons Electrons can only orbit in fixed distances

from the nucleus because they can only gain / lose a quanta of energy

This prevents the electron from “falling into” the nucleus

Problems with the Bohr model

1. The two postulates only work with the Hydrogen atom. When the model is applied to other atoms … extra dimensions of space is required.

2. The works of Grimaldi have shown that electrons are capable of displaying an interference pattern. How could a particle do this?

• Both of these problems can be “solved” to create a new theory by applying the works of deBroglie and Schrodinger.

Louis de Broglie

• First degree in History but applied for graduate work in Physics

• Doctoral thesis Recherches sur la théorie des quanta 

• Work beyond the intellect of his professors• Sent to Einstein who endorsed it fully

Matter Waves

De Broglie proposed that all matter have both matter properties and wave properties. Start with the Einstein energy-matter equality

E = mc2

This energy is quantized according to Planck So E = hf = mc2

hf = mc2

hf = (mc)c mc is the momentum of the wave = p

hf = pc v = fl

hf = p(fl)

h = plSo p = h / l

In short … any piece of matter travelling at any speed can exhibit wave properties

The effects for classical particles are too small to observe The electron is not only a particle but also

displays wave nature Therefore the electron can diffract

Light also displays both particle and wave nature

Bohr model – revision #1

The atom consists of A massive positively charged central nucleus Negatively charged electrons which create

standing waves of energy.These waves of energy can only vibrate / resonate at specific frequencies

These frequencies determine the orbitals around the nucleus

de Broglie matter waves do not solve the multi-dimensionality problem!

Enter Schrodinger

Einstein given the task to apply the Bohr/de Broglie model to atoms other than Hydrogen Was too busy working on GUT so he passed

the task on to his friend Erwin Schrodinger Schrodinger was an unpopular choice in that

he was considered a failed Physicist!

Christmas holidays and New Years 1925-26 Schrodinger takes his mistress into the Alps

on vacation It is here that he comes up with his wave

equation for all matterThis set of equations works for all atoms --- not just Hydrogen

The Schrodinger wave model

de Broglie’s matter waves do not describe the physical location of the electrons around the nucleus The mathematics describes the probability of

finding the electron in a given location of space

Loss of determinism?!?!?All life is based on probability … there are no definite knowns!

“God does not play dice with the Universe”

Implications of a Probabilistic Universe

Quantum tunneling

HUP

Schrödinger's cat

BEC

Separation of classical world and quantum world

Quantum Tunneling

Imagine that you have a single electron that you place into an electrical potential well. The electron requires an infinite amount of energy to climb out of the box.

Where is the electron?

Now imagine that you leave the electron and return to it a few weeks later.

Where is the electron now?

Classical Physics would tell us that the electron must always be in the electropotential well … since it doesn’t have enough energy to “climb out”

Experimental evidence indicates that the electron will leak out over time!!! This is the process through which

semiconductors work

The Schrodinger equation defining the position of the electron is both energy, and time dependent As time proceeds the probability of finding the

electron in a set location begins to smear out over space.

There is a probability that the electron can “climb out” of the electropotential well.

Heisenberg’s Uncertainty Principle

Two versions of HUP Uncertainty between knowing the momentum

of an object and the exact position of an object

Uncertainty between knowing the amount of energy a substance contains within a time interval of measurment

Momentum and position

Imagine that we have a small sub atomic particle that we want to observe and record all possible data for. We start to attempt to measure the

momentum of the object To measure the velocity (and therefore the

momentum) we need to set up a set of timing gates

We can use low energy x-rays to record the passage of the sub atomic particle from one gate to the other

This will allow us to measure the velocity and therefore the momentum

The wavelength of the x-ray is too long at low energies so even though we can use it to measure the momentum we can not use it to determine the exact position.

We can increase the energy of the x-ray which results in a tighter wavelength This will allow us to know the exact location of

our subatomic particleBut the increase in energy imparts energy to our sub atomic particle changing it’s motion direction …. And therefore changing the momentum

So By measuring the momentum the exact

position remains unknown By measuring the exact position we change

the momentum

We can not know the exact position and momentum at the same time.

A similar uncertainty exists between energy and time

Schrodinger’s Cat

The macroscopic / classical physicists rebuttal to HUP Classical physicists refuse to believe that

It is impossible to know everything about a system

The act of observing a system changes the system ... The act of experimentation destroys determinism