Bose Einstein Statistics Derivation Pdf Download
Arnau Cyr
The course materials are divided into 14 modules which can be accessed by clicking Course Modules on the left menu. A module will have several sections including the module-at-a-glance, readings, video lectures and related content, discussions, and quizzes. Students should regularly check the Calendar and Announcements for assignment due dates. Modules begin on Wednesdays and complete on Tuesdays.
The broad objective of the course is to provide the student with detailed understanding of the way in which statistical mechanics not only provides a clear derivation of the empirical laws of thermodynamics but also a framework for explicit computation of many thermal properties of bulk matter from microscopic models. By the end of the course the student should be able to apply thermodynamic principle to simple systems and calculate and analyze various thermodynamic properties of specific idealized classical and quantum systems using standard techniques such as the partition function.
- Explain the physical concepts and the laws of classical thermodynamics and derive relations connecting various thermodynamic properties of a single- component system.
- Apply thermodynamic relations to compute thermal properties of specific single component systems.
- Apply thermodynamic concepts to explain physical behavior of multi-component and multi-phase systems.
- Explain the postulates of statistical mechanics and derive the formal structure of thermodynamics from them.
- Explain and develop the ensemble theory for a Hamiltonian dynamical system.
- Apply the microcanonical ensemble to derive the complete thermodynamics of an ideal gas and a system of harmonic oscillators.
- Derive the complete formal structure of thermodynamics from the canonical ensemble.
- Employ the partition function to compute thermodynamic properties of specific systems in thermal equilibrium with a heat reservoir.
- Describe the thermodynamics of an equilibrium system exchanging both particles and energy with a reservoir in terms of the grand partition function.
- Apply the general theory of grand canonical ensemble and the grand partition function to derive the thermodynamics of a system of non-interacting indistinguishable particles obeying Bose-Einstein, Fermi-Dirac and classical Maxwell-Boltzmann statistics.
- Apply quantum statistical mechanics to derive thermodynamic properties of non- interacting quantum systems including ideal quantum gases and black body radiation.
- Apply thermodynamics of quantum systems to explain a variety of exotic phenomena involving ideal quantum gases.
Webcam, microphone (if provided with computer, this is usually adequate along with adequate lighting and no background sound interference). MS Office Suite (Word, Excel) An equation editor will be extremely helpful in completing the assignments in MS Word format. Another superior option is to produce the solution as a TeX document. Final submissions should be in the form of a PDF document.
Deadlines for Adding, Dropping and Withdrawing from Courses
Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar ( -services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.
Academic Misconduct Policy
All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.
Students with Disabilities - Accommodations and Accessibility
Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.
Student Conduct Code
The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically.
Classroom Climate
JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity.
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).
Bose and Saha became great friends. They studied mathematics together and were eventually appointed assistant lecturers in physics at the newly established University College of Science and Technology in Calcutta, founded in 1914. The pair had learned German, French, and English so that they could study the papers that were being written by Planck, Einstein, and other European scientists.
On the afternoon of Sunday, October 7, 1900, Heinrich Rubens had tea with Planck and told him about the latest experimental data on the blackbody spectrum that he and Ferdinand Kurlbaum had obtained. After Rubens left, Planck set about finding a mathematical formula that would fit the data. He succeeded with his formula,
Strong experimental evidence in favor of light quanta eventually emerged in 1923 from the Compton effect. The classical wave theory of radiation failed to explain the observed shifts in the wavelength of the scattered x-rays. Observation clearly pointed toward elementary processes of energy transfer between light quanta and the electrons in the atoms.
Nonetheless, his derivation of the first factor had to be supplemented by a factor of 2 due to the two states of polarization of light, which were not wholly quantum mechanical. Einstein observed in a postcard to Bose dated July 2,
Be that as it may, it could hardly have been foreseen at that time that a short paper, only about four pages long, without a single reference, would eventually have profound influence across a vast spectrum of physics.
There is one more fundamental particle that the Standard Model requires to generate the masses of leptons, which would otherwise be massless like the photon and fly away at the speed of light, making it impossible for atoms to form in the universe. That particle is a spin-0 boson. It was named the Higgs boson after Peter Higgs of the University of Edinburgh, though several other physicists proposed such a particle at more or less the same time as Higgs in 1964. It took nearly half a century and a multibillion-dollar particle accelerator, the Large Hadron Collider at CERN, to find it.
The Higgs boson was intrinsic to understanding of how lepton mass was generated in the Big Bang. In 1964, Arno Penzias and Robert Wilson, working with the Holmdel Horn Antenna at the Bell Labs in Princeton, accidentally discovered cosmic microwave background radiation, which was strong evidence in favor of a hot early universe, as implicated in the Big Bang theory, and against the rival steady-state theory. For this landmark discovery, Penzias and Wilson were awarded the 1978 Nobel Prize in Physics. It turns out that, according to precision observations carried out in 1994 by the Far Infrared Absolute Spectrophotometer aboard the Cosmic Background Explorer satellite, cosmic microwave background radiation has a pure Planck spectrum, signaling that it is blackbody radiation in thermal equilibrium at a temperature of 2.7K.
It was precisely the spectrum of blackbody radiation measured in labs in the last few years of the nineteenth century that led Planck to discover quantum theory in 1900. And it was this Planck spectrum that led Bose to discover the new statistics in 1924.
The fact that there are two classes of fundamental building blocks, bosons and fermions, rather than just one, has prompted physicists searching for unified theories of particles to propose a relationship between the two. This has become known as supersymmetry. If such a symmetry exists, it would bring the standoffish fermions and the clannish bosons together within the fold of a single family and would imply the existence of a lot of undiscovered particles. The latter could provide an elegant solution to many problem areas in the Standard Model. In supersymmetry, each boson and fermion would have an associated particle, termed a superpartner, in the other class. An electron, for example, which is a fermion, would have a superpartner called a selectron, its bosonic partner. In perfectly supersymmetric theories, each pair of superpartners would have the same mass and internal quantum numbers, except for their spin.
b1e95dc632