PHYS 445 Supplement - Quick and dirty quantum mechanics Supplement - Quick and dirty quantum mechanics for PHYS 445 What's Important: old quantum theory particle in a 1-D box rigid rotor harmonic oscillator Old quantum theory
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A very simple approach to
PHYS 445 Lecture 34 - Van der Waals equation Lecture 34 - Van der Waals equation What's Important: B2 for hard spheres B2 for attraction and repulsion van der Waals equation Text: Reif Second virial coefficient
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At the end of the previous lecture, w
PHYS 445 Lecture 32 - Ising model Lecture 32 - Ising model What's Important: Ising model in 3D Text: Reif Ising model
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In the previous lecture, we considered the effects of dimensionality on the existence of phase transitions, using a spin system as
PHYS 445 Lecture 31 - Interactions: Phase transitions Lecture 31 - Interactions: Phase transitions What's Important: galaxy formation galactic evolution Text: Reif Phase transitions
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Most of the systems considered so far in this course have consiste
PHYS 445 Lecture 30 - Low temperature Fermi gas Lecture 30 - Low temperature Fermi gas What's Important: heat capacity for ideal Fermi gas Text: Reif Heat capacity for ideal Fermi gas
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This lecture contains a somewhat lengthy mathematical examinatio
PHYS 445 Lecture 29 - Heat capacities in metals Lecture 29 - Heat capacities in metals What's Important: electrons in metals heat capacities Text: Reif Sec. 19.7; Kittel Chap. 7
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Heat capacities in metals are covered in two lectures. Here, the exper
PHYS 445 Lecture 28 - Superfluids Lecture 28 - Superfluids What's Important: 4 He condensation superfluids Bose-Einstein condensation Text: Reif
4
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He condensation
As 4He is cooled, it undergoes a phase transition to a liquid state (referred to as H
PHYS 445 Lecture 27 - Black-body radiation II Lecture 27 - Black-body radiation II What's Important: radiation pressure radiative power Text: Reif Radiation pressure The general definition of the mean force ln Z = h which for the mean pressure implies ln
PHYS 445 Lecture 26 - Black-body radiation I Lecture 26 - Black-body radiation I What's Important: number density energy density Text: Reif
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In our previous discussion of photons, we established that the mean number of photons with energy i is 1 ni
PHYS 445 Lecture 25 - T = 0 Fermi gas Lecture 25 - T = 0 Fermi gas What's Important: T = 0 Fermi gas metals neutron stars Text: Reif T=0 Fermi gas
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The previous lecture for the density of states in phase space dealt only with the energetics, not the
PHYS 445 Lecture 24 - Density of states Lecture 24 - Density of states What's Important: density of states in phase space Text: Reif Counting quantum states
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Some time back, we said that we needed to introduce a "density of states" factor in order t
PHYS 445 Lecture 23 - Fermions Lecture 23 - Fermions
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What's Important: Fermi-Dirac statistics comparisons among distributions Fermi energy Text: Reif
Fermi-Dirac statistics The Fermi-Dirac distribution can be handled in a similar way to the Bose-Ei
PHYS 445 Lecture 22 - Bosons Lecture 22 - Bosons What's Important: partition function number distribution condensation Text: Reif Boson partition function
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We now tackle the general problem of Bose-Einstein statistics. The situation is more difficul
PHYS 445 Lecture 21 - Indistinguishable particles Lecture 21 - Indistinguishable particles What's Important: number distributions for MB, photons. Text: Reif Secs. 9.4-9.7; skip 9.3
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In the previous lecture, we established that the mean number densi
PHYS 445 Lecture 20 - Quantum statistics Lecture 20 - Quantum statistics What's Important: quantum statistics Text: Reif Quantum statistics
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The quantum approach to mechanics can be formulated in a statistical form using expectation values or means.
PHYS 445 Lecture 19 - MB continued Lecture 19 - MB continued What's Important: pressure of an ideal gas Text: Reif Pressure of an ideal gas Our picture of an ideal gas hitting a wall is
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z - direction
With each collision, an amount of momentum 2mvz
PHYS 445 Lecture 18 - Maxwell-Boltzmann distribution Lecture 18 - Maxwell-Boltzmann distribution What's Important: mean speeds molecular flux Text: Reif Mean speeds
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The Maxwell-Boltzmann speed distribution that was derived in the previous lecture h
PHYS 445 Lecture 17 - Ideal gas in detail Lecture 17 - Ideal gas in detail What's Important: phase space of non-interacting particles Maxwell-Boltzmann distribution Text: Reif Phase space of non-interacting particles
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An ideal gas is one in which pa
PHYS 445 Lecture 16 - Quantum oscillators Lecture 16 - Quantum oscillators What's Important: quantum oscillator at T > 0 continuous quantum states Text: Reif Quantum oscillators
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In the previous lecture we used the classical equipartition theorem to
PHYS 445 Lecture 14 - Grand canonical ensemble Lecture 14 - Grand canonical ensemble What's Important: weakly interacting systems entropy and probability grand canonical ensemble Text: Reif
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Secs. 6.7 and 6.8 on approximation techniques can be read
PHYS 445 Lecture 13 - Partition function Z Lecture 13 - Partition function Z What's Important: partition function fluctuations and specific heat work and Z entropy and Z Text: Reif Partition function
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The sum over the Boltzmann factors exp(-Er) appe
PHYS 445 Lecture 12 - Ensembles Lecture 12 - Ensembles
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What's Important: ensembles spin - 1/2 particles in a magnetic field Text: Reif Demonstrations: magnet and compasses on an overhead projector magnetization and temperature - use Monel (Ni+Cu) a
PHYS 445 Lecture 10 - Systems in thermal contact Lecture 10 - Systems in thermal contact What's Important: heat flow heat reservoirs thermal contact mechanical contact Text: Reif Heat flow (not covered in class)
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This result is rather intuitive, but
PHYS 445 Lecture 9 - Temperature and specific heat Lecture 9 - Temperature and specific heat What's Important: thermal equilibrium temperature zeroth law of thermodynamics equipartition theorem specific heat of an ideal gas Text: Reif Approach to equilibr
PHYS 445 Lecture 8 - Interacting systems Lecture 8 - Interacting systems What's Important: equilibrium and reversibility systems in interaction Text: Reif
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Constraints and
(Reif, Sec. 3.1; not covered in class)
Suppose that two systems are brought in c
PHYS 445 Lecture 6 - Classical ideal gas Lecture 6 - Classical ideal gas What's Important: classical phase space Text: Reif Classical ideal gas
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In the previous lecture, we introduced the concept of accessible states, with the number of accessible stat