#the “time invariant schrodinger equation”

[sparkofthetelling]

my quantum mechanics professor: "a good quantum number is one that conserves with the hamiltonian"

me, woke, tumblr user: "what if we just didn't moralize quantum numbers and described them simply by their properties"

[mamtajuyal1986]

IIT JAM 2020 Physics (PH) Syllabus | IIT JAM 2020 Physics (PH) Exam Pattern

IIT JAM 2020 Physics (PH) Syllabus | IIT JAM 2020 Physics (PH) Exam Pattern Physics (PH): The syllabus is a very important aspect while preparing for the examination. Therefore it is advised to all the appearing candidates that they should go through the Physics (PH) syllabus properly before preparing for the examination. Mathematical Methods: Calculus of single and multiple variables, partial derivatives, Jacobian, imperfect and perfect differentials, Taylor expansion, Fourier series. Vector algebra, Vector Calculus, Multiple integrals, Divergence theorem, Green's theorem, Stokes' theorem. First order equations and linear second order differential equations with constant coefficients. Matrices and determinants, Algebra of complex numbers. Mechanics and General Properties of Matter: Newton's laws of motion and applications, Velocity and acceleration in Cartesian, polar and cylindrical coordinate systems, uniformly rotating frame, centrifugal and Coriolis forces, Motion under a central force, Kepler's laws, Gravitational Law and field, Conservative and non-conservative forces. System of particles, Center of mass, equation of motion of the CM, conservation of linear and angular momentum, conservation of energy, variable mass systems. Elastic and inelastic collisions. Rigid body motion, fixed axis rotations, rotation and translation, moments of Inertia and products of Inertia, parallel and perpendicular axes theorem. Principal moments and axes. Kinematics of moving fluids, equation of continuity, Euler's equation, Bernoulli's theorem. Oscillations, Waves and Optics: Differential equation for simple harmonic oscillator and its general solution. Superposition of two or more simple harmonic oscillators. Lissajous figures. Damped and forced oscillators, resonance. Wave equation, traveling and standing waves in one-dimension. Energy density and energy transmission in waves. Group velocity and phase velocity. Sound waves in media. Doppler Effect. Fermat's Principle. General theory of image formation. Thick lens, thin lens and lens combinations. Interference of light, optical path retardation. Fraunhofer diffraction. Rayleigh criterion and resolving power. Diffraction gratings. Polarization: linear, circular and elliptic polarization. Double refraction and optical rotation. Electricity and Magnetism: Coulomb's law, Gauss's law. Electric field and potential. Electrostatic boundary conditions, Solution of Laplace's equation for simple cases. Conductors, capacitors, dielectrics, dielectric polarization, volume and surface charges, electrostatic energy. Biot-Savart law, Ampere's law, Faraday's law of electromagnetic induction, Self and mutual inductance. Alternating currents. Simple DC and AC circuits with R, L and C components. Displacement current, Maxwelll's equations and plane electromagnetic waves, Poynting's theorem, reflection and refraction at a dielectric interface, transmission and reflection coefficients (normal incidence only). Lorentz Force and motion of charged particles in electric and magnetic fields. Kinetic theory, Thermodynamics: Elements of Kinetic theory of gases. Velocity distribution and Equipartition of energy. Specific heat of Mono-, di- and tri-atomic gases. Ideal gas, van-der-Waals gas and equation of state. Mean free path. Laws of thermodynamics. Zeroth law and concept of thermal equilibrium. First law and its consequences. Isothermal and adiabatic processes. Reversible, irreversible and quasi-static processes. Second law and entropy. Carnot cycle. Maxwell's thermodynamic relations and simple applications. Thermodynamic potentials and their applications. Phase transitions and Clausius-Clapeyron equation. Ideas of ensembles, Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein distributions. Modern Physics: Inertial frames and Galilean invariance. Postulates of special relativity. Lorentz transformations. Length contraction, time dilation. Relativistic velocity addition theorem, mass energy equivalence. Blackbody radiation, photoelectric effect, Compton effect, Bohr's atomic model, X-rays. Wave-particle duality, Uncertainty principle, the superposition principle, calculation of expectation values, Schrodinger equation and its solution for one, two and three dimensional boxes. Solution of Schrodinger equation for the one dimensional harmonic oscillator. Reflection and transmission at a step potential, Pauli exclusion principle. Structure of atomic nucleus, mass and binding energy. Radioactivity and its applications. Laws of radioactive decay. Solid State Physics, Devices and Electronics: Crystal structure, Bravais lattices and basis. Miller indices. X-ray diffraction and Bragg's law; Intrinsic and extrinsic semiconductors, variation of resistivity with temperature. Fermi level. p-n junction diode, I-V characteristics, Zener diode and its applications, BJT: characteristics in CB, CE, CC modes. Single stage amplifier, two stage R-C coupled amplifiers. Simple Oscillators: Barkhausen condition, sinusoidal oscillators. OPAMP and applications: Inverting and non-inverting amplifier. Boolean algebra: Binary number systems; conversion from one system to another system; binary addition and subtraction. Logic Gates AND, OR, NOT, NAND, NOR exclusive OR; Truth tables; combination of gates; de Morgan's theorem. Related Articles: IIT JAM 2020 Syllabus Biotechnology (BT) Syllabus Biological Sciences (BL) Syllabus Chemistry (CY) Syllabus Geology (GG) Syllabus Mathematics (MA) Syllabus Mathematical Statistics (MS) Syllabus Physics (PH) Syllabus Read the full article

[arxt1]

On the time evolution of cosmological correlators. (arXiv:2009.07874v1 [hep-th])

Developing our understanding of how correlations evolve during inflation is crucial if we are to extract information about the early Universe from our late-time observables. To that end, we revisit the time evolution of scalar field correlators on de Sitter spacetime in the Schrodinger picture. By direct manipulation of the Schrodinger equation, we write down simple "equations of motion" for the coefficients which determine the wavefunction. Rather than specify a particular interaction Hamiltonian, we assume only very basic properties (unitarity, de Sitter invariance and locality) to derive general consequences for the wavefunction's evolution. In particular, we identify a number of "constants of motion": properties of the initial state which are conserved by any unitary dynamics. We further constrain the time evolution by deriving constraints from the de Sitter isometries and show that these reduce to the familiar conformal Ward identities at late times. Finally, we show how the evolution of a state from the conformal boundary into the bulk can be described via a number of "transfer functions" which are analytic outside the horizon for any local interaction. These objects exhibit divergences for particular values of the scalar mass, and we show how such divergences can be removed by a renormalisation of the boundary wavefunction - this is equivalent to performing a "Boundary Operator Expansion" which expresses the bulk operators in terms of regulated boundary operators. Altogether, this improved understanding of the wavefunction in the bulk of de Sitter complements recent advances from a purely boundary perspective, and reveals new structure in cosmological correlators.

from gr-qc updates on arXiv.org https://ift.tt/2ZLTH99

[positivederivative]

June 05, 2017 at 04:52AM

Today I Learned: 1) Gague theory! I mean, I didn't learn all of Gague theory, but I learned a bit about it, and a particularly startling piece of physics. Gague theory starts with an observation of the global invariance of the wave function to phase changes. Let's break that down a bit. Quantum mechanics is all about the wave function of a particle -- basically a function that describes how "much" a particle is located at every point in space. The larger the value of the wave function at a point, the more likely it is you'll find that particle there if you try to measure its position. You may have heard of the Schrodinger equation -- that's the function that describes how the wave function changes over time. The thing is, though, the wave function is a *complex* function. Not complex in the sense that it's complicated, but complex in the sense that it's complex-valued -- its value at a point is a complex number, not a (strictly) real number. The best way to think of it is that there's a little wave function arrow at every point in space that spins around in a circle and grows and shrinks. The length of the arrow determines how "much" the particle is there. The direction of the arrow is called its *phase*. The Schrodinger equation determines how the arrows grow, shrink, and spin over time. When particle physicists talk about the "global phase invariance" of a wave function, they mean that it doesn't really matter which way the arrows point, as long as their *relative* phases are unchanged. If you take every arrow at every point and spin it around a half-turn, nothing changes. The Schrodinger equation, as it was originally written down, guarantees global phase invariance of the wave function by its construction. There's a more extreme kind of phase invariance, though -- *local* phase invariance. If the wave equation is locally phase-invariant, that means that you can grab all the arrows in a very small space (a "local region", if you will) and spin *them* by an arbitrary amount, and nothing changes physically. In general, the Schrodinger equation does *not* guarantee local phase invariance -- if you change the phase of the wave equation in only a small region, without changing the rest of the universe's wave function, you get a different physical system that you would make different predictions about. Gague theory started with an attempt by physicists Yang and Mills to make a version of the Schrodinger equation that was invariant to local phase change. The classical Schrodinger equation doesn't do it, but it turns out that you can add a correction term to the equation that makes it so it *is* invariant to local phase changes. So they added it. "Wait, what?" you might rightly ask at this point. "How come they can just ADD a term to the Schrodinger equation like that?". Normally, that would be kind of crazy... but it turns out that the correction term you need to get local invariance to phase changes is EXACTLY a term that describes the effect of electromagnetism. Let me repeat that: Assuming invariance to local phase change in the Schrodinger *necessarily* causes electromagnetism to pop out. That's all you need. Another nice little bonus comes from local phase change via Nother's Theorem -- local phase change invariance is mathematcially equivalent to conservation of charge. So yeah. Electromagnetism can be explained *entriely* by invariance of the wave equation to local phase change. Next time someone claims that scientists don't know why magnets work, you can now laugh at them properly. 2) Zero calorie noodles are emphatically not amazing. They don't really taste like anything, and they have a weird crispy/slimy texture that kind of reminds me of jellyfish, and not in a good way. They also smell particularly bad right out of the package, though the smell does wash off pretty easily and didn't make it into the final dish. 3) IKEA's Lack tables are actually made of cardboard. By which I don't mean "a cardboard like wood-adjacent material". I mean cardboard, honecombed inside a thin shell of plywood. That's how it's so ridiculously light and cheap (and strong, for its weight) -- and also why it's one of the most flammable furnitures known to mankind.