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FI 3103 Quantum Physics

Alexander A. Iskandar

Physics of Magnetism and Photonics Research Group

Institut Teknologi Bandung

General Information Lecture schedule

• 17 18 9136

• 51 52 9221

Tutorial • Teaching Assistant : Mr. Suhandoko D. Isro

• 57 58 BSC A

• During the tutorial there will be several Quizzes and average mark of the Quizzes will taken as one of the component of the Final Mark

Walk Out time : 20 minutes

Textbook • S. Gasiorowicz, Quantum Physics 3rd ed.,

John Wiley 2003

Alexander A. Iskandar 2

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General Information

Alexander A. Iskandar 3

Evaluation : • A Midterm Exam (week 7) and a Final Exam

Expected Exam Answer : • Answer should show good understanding of the physical phenomena

considered in the problem, as evident by sound arguments and clear and correct steps in finding the solution.

• The use of correct formulas and notation (vector and scalar, integrals, complex) and the right units.

• Final correct numerical value (if asked).

Slide download (weekly basis): • http://fismots.fi.itb.ac.id

The Emergence of Quantum Physics

Black Body Radiation

Photoelectric Effect

Compton Effect

Alexander A. Iskandar Emergence of Quantum Physics 4

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(Modern) Physics in early 20th century 19th century physicists thought they had it all together.

They had complete understanding of classical (Newton) mechanics that govern particles to planetary movement.


Newton promoted the corpuscular (particle) theory of light. Particles of light travel in straight lines or rays, which explained sharp shadows, reflection and refraction

(Modern) Physics in early 20th century They found that it turns out electricity and magnetism are one

of the same interaction, and Maxwell realized that light is a wave.


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Further proved by interference and dif-fraction promoted by Huygens and Fresnel.

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http://en.wikipedia.org/wiki/File:Newton_Opticks_titlepage.jpg

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(Modern) Physics in early 20th century They introduced the concept of thermal equilibrium,

established heat as energy, introduced the concept of internal energy, created temperature as a measure of internal energy. Realized limitations: some energy processes cannot take place.


(Modern) Physics in early 20th century But they were surprised to find that several new experimental

results were very weird that could not be explained with classical physics.

Modern physics is the story of these surprises, surprises that have changed the world beyond all recognition.

Understanding of these surprises lead to a new physics : the (old) quantum physics.

The following lecture will give you a summary of these unexplained phenomena.


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When matter is heated, it not only absorbs light, but it also spontaneously emits it.

A blackbody is a cavity with a material that only emits thermal radiation. Incoming radiation is absorbed in the cavity.

Blackbodies are interesting because their optical properties are independent of the material and only depend on the temperature.

Blackbody radiation


Blackbody radiation


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Wien’s Displacement Law The spectral intensity I(l, T) is the total power

radiated per unit area per unit wavelength at a given temperature.


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Wilhelm Wien (Phys. 1911)

Wien’s displacement law: The maximum of the spectrum shifts to smaller wavelengths as the temperature is increased.

Stefan-Boltzmann Law The total power radiated increases

with the temperature:


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Jozef Stefan Ludwig Boltzman

This is known as the Stefan-Boltzmann law, with the constant σ experimentally measured to be 5.6705 × 10−8 W / (m2 · K4).

The emissivity e (e = 1 for an idealized blackbody) is simply the ratio of the emissive power of an object to that of an ideal blackbody and is always less than 1.

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Rayleigh-Jeans Formula Lord Rayleigh used the classical theories

of electromagnetism and thermodynamics to show that the blackbody spectral distribution should be:


I It approaches the data at longer

wavelengths, but it deviates badly at short wavelengths. This problem for small wavelengths became known as the ultraviolet catastrophe and was one of the outstanding exceptions that classical physics could not explain.

James Jeans Lord Rayleigh (Phys. 1904)

Planck’s Radiation Law Planck assumed that the radiation in the cavity was

emitted (and absorbed) by some sort of “oscillators.” He used Boltzman’s statistical methods to arrive at the following formula that fit the blackbody radiation data.


Planck made two modifications to the classical theory: • The oscillators (of electromagnetic origin) can only have certain

discrete energies, En = nhn, where n is an integer, n is the frequency, and h is called Planck’s constant:

h = 6.6261 × 10−34 J·s.

• The oscillators can absorb or emit energy in discrete multiples of the fundamental quantum of energy given by

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Max Planck (Phys. 1918)

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PhET: photoelectric

Photoelectric Effects Hertz showed that when UV light is shone on a metal

plate in a vacuum, it emits charged particles.


Classical predictions: • Electric field E of light exerts

force F = -eE on electrons. As intensity of light increases, force increases, so KE of ejected electrons should increase.

• Electrons should be emitted whatever the frequency n of the light, so long as E is sufficiently large

• For very low intensities, expect a time lag between light exposure and emission, while electrons absorb enough energy to escape from material.

H. Hertz

Photoelectric Effects The actual results

• Maximum KE of ejected electrons is independent of intensity, but linearly dependent on n

• For n < n0 (i.e. for frequencies below a cut-off frequency) no electrons are emitted

• There is no time lag. However, rate of ejection of electrons depends on light intensity


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Einstein’s Theory Einstein take Planck’s theory one step further.

Einstein suggested that the electromagnetic radiation field is quantized into particles called photons.

Each photon has the energy quantum:

or, with

An electron absorbs a single photon to leave the material.

Conservation of energy yields:


A. Einstein (Phys. 1905)

E hn E / 2h

where f is the work function of the metal (potential energy to be overcome before an electron could escape).

Verified in detail through subsequent experiments by Millikan.

f KEh R. Millikan

Einstein’s Theory Electrons are bound in the target

material by electric forces, therefore they need some minimum energy before they will get ejected at all (i.e., ejected with zero kinetic energy)

The energy of the incoming photon goes into freeing the electron and then whatever energy remains goes into giving the electron some kinetic energy

The maximum kinetic energy can be measured by the stopping potential.


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Thomson Scattering Thomson scattering is the elastic scattering of

electromagnetic radiation by a free charged particle, as described by classical electromagnetism.

It is just the low-energy limit of Compton scattering: the particle kinetic energy and photon frequency are the same before and after the scattering.

This limit is valid as long as the photon energy is much less than the mass energy of the particle: hn << mc2.


J.J. Thomson

Thomson Scattering The electric field of the incident

wave (photon) accelerates the charged particle, causing it, in turn, to emit radiation at the same frequency as the incident wave, and thus the wave is scattered.

In this non-relativistic case, the main cause of the acceleration of the particle will be due to the electric field component of the incident wave, and the magnetic field can be neglected.


q

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Thomson Scattering The particle will move in the

direction of the oscillating electric field, resulting in electromagnetic dipole radiation. The moving particle radiates most strongly in a direction perpendicular to its motion and that radiation will be polarized along the direction of its motion.

Therefore, depending on where an observer is located, the light scattered from a small volume element may appear to be more or less polarized.


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Thomson Scattering The electric fields of the

incoming and observed beam can be divided up into those components lying in the plane of observation (formed by the incoming and observed beams) and those components perpendicular to that plane. Those components lying in the plane are referred to as "radial" and those perpendicular to the plane are "tangential", since this is how they appear to the observer.


q

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Thomson Scattering The diagram on the right shows the

radial component of the incident electric field causing a component of motion of the charged particles at the scattering point which also lies in the plane of observation.

It can be seen that the amplitude of the wave observed will be proportional to the cosine of q, the angle between the incident and observed beam.


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The intensity, which is the square of the amplitude, will then be diminished by a factor of cos2(q). It can be seen that the tangential components (perpendicular to the plane of the diagram) will not be affected in this way.

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Compton Scattering Compton (1923) measured intensity of scattered X-

rays from solid target, as function of wavelength for different angles.


A. Compton (Phys. 1927)

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Compton Scattering Compton found that

the peak in scattered radiation shifts to longer wavelength than source. Amount depends on q (but not on the target material).



Compton Scattering


Treating the light as particle (photon) which has momentum, Compton explains the results by assuming “billiard ball” in-elastic collisions between particles of light (X-ray photons) and electrons in the material.


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Compton Scattering


The photon momentum is derived from relativistic energy-momentum relation:

Using the definition of speed

Since the speed of light is vacuum is always c, then the momentum of a photon is given by


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Compton Scattering


Conservation of momentum

Conservation of energy


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Compton won the 1927 Nobel Prize in Physics.

Compton Scattering



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