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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: 33

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.

### Noise reduction using interferometry

Consider a Mach-Zehnder interferometer where in one arm we place a filter with a transmission coefficient f << 1. The system is set up such that at one detector site we have constructive interference and at the other side we have destructive interference. Demonstrate that the expected number of detected photons N needed before a

### Einstein Summation and Levi-Civita Tensor

Please help answer this question. It requires you to give proof that two definitions of angular momentum are equal. The question is in the attachment. It is taken from this site. http://farside.ph.utexas.edu/teaching/qmech/Quantum/node80.html

### Lagrangian interaction and Feyman propagator

1. Consider a real scalar field phi with interaction Largrangian L_int = (p/(3!))phi^3. What is the mass dimension of u? Evaluate the leading u-dependent contributions to the following equation: (see attached file)

### 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.

### Problems with Variable Names

Provided is a list of variable names. Determine what is wrong (if anything) with each variable name and how to fix it. - two_wheels - BTUs-2-watts - loop - Another*variable - stDDev - mean.

### Residues Theorem and Integration of the function 1/(1+x^2)

Using the Residues Theorem, calculate the following: Integral limits between negative infinity and positive infinity [dx/(1+x^2)]. Please the file attached for the formula in its adequate notation.

### Proving Factorial Equations Involving Double Factorials

In many problems in mathematical physics, particularly in connection with Legendre polynomials (Chapter 12), we encounter products of the odd positive integers and products of the even positive integers. For convenience, these are given special labels as double factorials: 1*3*5***(2n + 1) = (2n + 1)!! 2*4*6***(2n) = (2n)!

### Time Required.

How much time is required before a 10 mCi sample of 99mTc (T1/2=6.0 hours) and a 25 mCi sample of 113m In (T1/2=1.7 hours) possess equal activities? Please see the attach file.

### 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

### Center of mass of meter sticks

Three uniform meter sticks, each of mass m, are placed on the floor as follows: stick 1 lies along the y axis from y = 0.350 m to y = 1.35 m, stick 2 lies along the x axis from x = 0.130 m to x = 1.13 m, stick 3 lies along the x axis from x = 1.41 m to x = 2.41 m. Calculate the location of the center of mass of the meter sticks.

### As a result of a chemical spill, benzene is evaporating at the rate of 1 gram per minute into a room that is 6 m * 6 m * 3 m in size and has a ventilation of 10 m3/min.

As a result of a chemical spill, benzene is evaporating at the rate of 1 gram per minute into a room that is 6 m * 6 m * 3 m in size and has a ventilation of 10 m3/min. a- Compute the steady state concentration of benzene in the room. b- Assuming the air in the room is initially free of benzene, compute the time necessary fo

### Dynamics: Springs and Oscillations

The 0.5 lb weight is suspended from a rigid frame as shown in the attached diagram. Pin A at the end of the rotating arm OA engages a slot in the frame, causing the frame to oscillate in the vertical direction. The arm is accelerated uniformly from rest at t = 0 and θ = 0 at the ω.(dot) = 100 rad/s^2. (2) Use numerical int

### Tuning Frequency Changes

In each problem one of its numerical parameters depends on 3504529. Divide 3504529 by 8 and depending on a value of a remainder, R, choose a corresponding value of this parameter. Use C = 4 5 6 7 8 9 10 11 For R = 0 1 2 3 4 5 6 7 The tuning frequency f of an

### The Period of Pvhysical Pendulum

A large bell is hung from a wooden beam so it can swing back and forth with negligible friction. The center of mass of the bell is 0.50m below the pivot, the bell has mass 38.0kg , and the moment of inertia of the bell about an axis at the pivot is 20.0kg*m^2. The clapper is a small, 1.8kg mass attached to one end of a slender

### Showing that a Matrix is Unitary

1) Show that the matrix is unitary. (Please see attached document for matrix.) 2) Find the eigenvalues of this matrix (they are not real numbers) and the eigenvectors. Please see the attached file for full question.

### 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.

### Critical Point on Van der Waals Isotherms

The critical point is the unique point on the original van der Waals isotherms (before the Maxwell construction) where both the first and second derivatives of P with respect to V (at fixed T) are zero. Use this fact to show that: V_c = 3Nb, P_c = (1/27) (a/b2), kT_c = (8/27) (a/b).

### 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.

### What is the x coordinate of the center of mass of the system

See attached file for full problem description with diagram. What is the x coordinate of the center of mass of the system described in Part D? Express your answer in terms of . =

### Mathematical Methods in Physical Sciences

I need some help on this question, it is from the book "The mathematical methods in the physical sciences". 7. Given v = x^2i + y^2j + z^2k a. Integrating v*ndo for surface of the cube which its length is 1 and is consisted of 4 vertexes of (0,0,0), (0,0,1), (0,1,0), (1,0,0). b. Using divergence theorem, calculate the abov

### Using dimensional analysis, which equation is (a -> m/^2, v -> m/s, x -> m , t -> s)

Using dimensional analysis, which one of the following equations is (a -> m/^2, v -> m/s, x -> m , t -> s) a. x = v/t b. v = 2ax t2 = x/a c. x2 = 2av d. x = at

### A person moves: What is the displacement from the original position?

A person moves 30m north, then 20m east and then 30 H (square root 2) m 45 degrees south of west. His displacement from the original position is a. 14m south west b. 10m west c. 28 m south d. 15 m east

### A floating spherical shell in water

A hollow spherical iron shell floats almost completely submerged in water. The outer diameter is 54.0 cm, and the density of iron is 7.87 g/cm3. Find the inner diameter. I have no clue how to start or solve this problem. Thanks for the help!

### Compare a graph of someone walking toward a motion detector and a graph of someone walking away.

For a distance vs. time plot, A) Compare a graph of someone walking at a constant slow pace and a graph of someone walking at a constant fast pace. How are they similar? How are they different? B) Compare a graph of someone walking toward a motion detector and a graph of someone walking away. How are they similar? How are

### 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

### Separation of Quasi and Intrinsic Fermi Levels and Conductivity

An undoped Si sample is optically excited at 300K such that Gop=10^19 ehp/cm^3s and taun=taup=1 microseconds. (a) What is the separation of the quasi Fermi levels (Efn-Efp)? (b) Where is Efn and Efp with respect to the intrinsic Fermi level Ei? (c) What is the change in conductivity due to excess carriers? What are the a

### 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.

### Given x,y coordinates of three point masses, find the center of mass, c.m.

Three point masses are located in an x,y plane as follows: M1= 7 kg, at (x1, y1)= (5, 6); M2= 8 kg, at (x2, y2)= (-4, 6); and M3= 9 kg, at (x3, y3)= (3, -2). Find the coordinates (xcm, ycm) of the c.m. of the system.