Author: Tru Physics
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Ohm’s Law
Introduction Ohm’s law is a fundamental principle in the field of electronics and electrical engineering. Named after the German physicist Georg Simon Ohm, it describes how current, voltage, and resistance interact in an electrical circuit. Definition and Equation Ohm’s law states that the current flowing through a conductor between two points is directly proportional to…
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Nuclear Fusion
Introduction Nuclear fusion is a process where two light nuclei combine to form a single, heavier nucleus. It’s the same process that powers the sun and other stars. This process releases a significant amount of energy due to the difference in binding energy between the initial and final products. Definition and Equation The general equation…
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Nuclear Fission
Introduction Nuclear fission is a nuclear reaction or a radioactive decay process in which the nucleus of an atom splits into two or more smaller, lighter nuclei. This process often releases a large amount of energy and usually one or more neutrons. Definition and Equation The nuclear fission reaction can be written generally as: where:…
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Lorentz Force
Introduction The Lorentz Force is a fundamental concept in electromagnetism, describing the force experienced by a charged particle moving in an electromagnetic field. It is named after the Dutch physicist Hendrik Lorentz who first derived the force law. Definition and Equation The Lorentz Force on a charged particle is given by the vector sum of…
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Problem 7.3 – Griffith’s Intro to QM
Problem 7.3 Two identical spin-zero bosons are placed in an infinite square well (Equation 2.22). They interact weakly with one another, via the potential (where is a constant with the dimensions of energy, and is the width of the well). (a) First, ignoring the interaction between the particles, find the ground state and the first…
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Problem 7.2 – Griffith’s Intro to QM
Problem 7.2 For the harmonic oscillator , the allowed energies are where is the classical frequency. Now suppose the spring constant increases slightly: . (Perhaps we cool the spring, so it becomes less flexible.) (a) Find the exact new energies (trivial, in this case). Expand your formula asa power series in , up to second…
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Problem 7.1 – Griffith’s Intro to QM
Problem 7.1 Suppose we put a delta-function bump in the center of the infinite square well: where is a constant. (a) Find the first-order correction to the allowed energies. Explain why the energies are not perturbed for even n. (b) Find the first three nonzero terms in the expansion (Equation 7.13) of the correction to…
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Problem 5.5 – Griffith’s Intro to QM
Problem 5.5 (a) Write down the Hamiltonian for two noninteracting identical particles in the infinite square well. Verify that the fermion ground state given in Example 5.1 is an eigenfunction of , with the appropriate eigenvalue. (b) Find the next two excited states (beyond the ones given in the example)—wave functions, energies, and degeneracies—for each…
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Problem 5.4 – Griffith’s Intro to QM
Problem 5.4 (a) If and are orthogonal, and both are normalized, what is the constant in Equation 5.17? (b) If (and it is normalized), what is ? (This case, of course, occurs only for bosons.) Solution: Problem 5.4 Solution (Download)
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Problem 5.3 – Griffith’s Intro to QM
Problem 5.3 Chlorine has two naturally occurring isotopes, and Show that the vibrational spectrum of HCl should consist of closely spaced doublets, with a splitting given by , where is the frequency of the emitted photon. Hint: Think of it as a harmonic oscillator, with where is the reduced mass (Equation 5.15) and is presumably…