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Mathematical Physics

Mathematical physics is the study of mathematical methods for application of problems in physics. There are five distinct branches of mathematical physics: geometrically advanced formulation of classical mechanics, partial differential equations, quantum theory, Relativity and Quantum Relativistic Theories and statistical mechanics. Each branch has its own section of physics problems in which it corresponds to.

Mathematical physics is denoted by the nature of research. The research is aimed at studying and solving problems inspired by physics within a mathematically rigorous framework. Therefore, mathematical physics can cover a broad range of topics from pure mathematics to theoretical physics. Mathematical physicist does not conduct experiments like “regular” physicists do. The advent of the computer has created a new application of mathematical physics however that allows highly complex simulations being conducted. These simulations are run off of complex mathematical models to model certain phenomena.

Categories within Mathematical Physics

Statistical Mechanics

Postings: 32

Statistical Mechanics is the branch of physics which applies probability theory to study thermodynamic behavior of systems composed of a large number of particles.

Partial Differential Equation

Postings: 25

A partial differential equation is a differential equation which contains unknown multivariable functions and their partial derivatives.

Summation of Divergent Series

In physics one often needs to sum divergent series. Here we give a simple example of how one can estimate the limit of x to infinity of a function f(x) given by its Taylor expansion around x = 0 when its radius of convergence is only 1.

Interference of 2 Waves.

Two loudspeakers are placed side by side a distance d=4.00m apart. A listener observes maximum constructive interference while standing in front of the loudspeakers, equidistant from both of them. The distance from the listener to the point halfway between the speakers is l=5.00m. One of the loudspeakers is then moved dir

Determining the moment of inertia of a pendulum

The pendulum shown in the figure (see attachment) consists of a thin disk and two slender rods. The disk has a mass of 2 kg, the longer rod AB has a mass of 6.5 kg and the shorter rod CD has a mass of 2.5 kg. Determine the moment of inertia of the pendulum about an axis perpendicular to the page passing through (a) point O, and

Four Masses

Please see problem attached. The four masses shown in Figure Ex13.17 are connected by massless, rigid rods, with m = 184 g. (a) Find the coordinates of the center of mass. (b) Find the moment of inertia about a diagonal axis that passes through masses B and D.

Pendulum Motion: Lagrangian Generalized Coordinates

Consider the pendulum of figure 7.4, suspended inside a railroad car, but suppose that the can is oscillating back and forth, so that the point of suspension has position x=Acos(wt), y=0. Use the angle Φ as the generalized coordinate and write down the equations that give the Cartesian coordinates of the bob in terms of Φ and

Gaussian Distribution and Fourier Transforms

1. The Fourier Transform of the probability density, P(x) is + T(k) =  (e^(ikx)}*P(x) dx - and is called the characteristic function of the random variable x. Let F(k) = log (T(k)) and show that a) F(0) = 0 b) F'(0) = i<x> c) F'' (0) = i<(x)^2> 2. Take P(x) to be the G

Recoil Force of a Gun

A soldier on a firing range fires an 8-shot burst from an assault weapon at a full automatic rate of 1000 rounds per minute. Each bullet has a mass of 7.42 g and a speed of 295 m/s relative to the ground as it leaves the barrel of the weapon. a). Calculate the average recoil force (in N) exerted on the weapon during that burs

Planetary motion: Show that h = |dr/dt|^2/2 - &#956;/r is a constant.

Starting from the formula d^r/dt^2 = -&#956; (r/r^3) show by differentiation that the quantity h = |dr/dt|^2/2 - &#956;/r is a constant. It is useful to recall that |dr/dt|^2 = dr/dt . dr/dt. You will need to use your calculus skills to find an expression for the derivative of 1/r with respect to time t, after which the fact tha

Moments of Inertia

Show that none of the principal moments of inertia can exceed the sum of the other two.

Density of an unknown material 10/19

A solid cube of unknown composition is seen floating upright in water with 30% of it above the surface. What is the density of the material? I believe the answer is 0.70 g/cm^3.

Flow Rate

A rectangular open tank is 4.5' wide, 3' deep and 6' long. We wish to fill the tank using a 1" diameter hose that delivers water at a speed of 100 inch/s. a) Determine the volume of the tank in gallons and liters. b) Compute the volume of water delivered by the hose in bothe quarts and liters per second. c) How long will i

Kinetic Friction

Which of these mathematical expressions have the appropriate dimensions of the coefficient of kinetic friction? Please see attached for mathematical expressions. Type the letters corresponding to correct answers alphabetically. Do not use commas. For instance, if A, B, and D have the appropriate dimensions, enter ABD.

Locating the Centroid

Question: Locate the centroid y of the area whose equation is y=1/x bounded by the x axis, and the line x=.5 inches. The height of the area starts at 2 inches high at x=.5 inches, and slopes down to 0.5 inches high at x=2 inches. The length of the shape is 1.5 inches.

Centroid of ellipse

Half of an ellipse is centered with x, y, and z axis' passing through. The nose extends out towards the y axis at a distance b. It's circular base has radial height 'a' from the x axis. Locate the centroid of the ellipsoid of revolution whose equation is y^2/b^2 + z^2/a^2 = 1.

Direction of Cosines

Okay I have been racking my brain with this one for over a week and still have no clue how to do this.I need to study this for a test I am having and can't seem to figure this out Consider an arbitrary 3D vector: A=Axx+Ayy+Azz a) Determine the direction cosines for this vector. These are cos[&#61537;], cos[&#61538;] and

Finding Speed

Two planes leave simultaneously from the same airport, one flying due north and the other flying due east. The north bound plane is flying 50 miles per hour faster than the east bound plane. After 3 hours the planes are 2,440 miles apart. Find the speed of each plane. I made a guess at it because I really don't know how to figu

Double pendulum Calculations

A double pendulum consists of a pendulum of mass m2 hanging from a pendulum of mass m1. The motion of both parts of the double pendulum is constrained to the x-y plane. Both strings are "unstretchable" and having length I2 and I1, respectively. a) How many degrees of freedom does this system have? Using the variable theta1

Operators and Eigenstates

If |0> and |1> denote the two eigenstates of N corresponding to the eigenvalues 0 and 1, respectively, show that câ?  |0> = |1> and c |0> = 0

Determining Center of Mass

Find the center of mass of a system of three particles of mass 2 kg, 3kg and 4 kg placed at the corners of an equilateral triangle of side 2 meters.