Homework Statement
An R-branch of a band of a ^1\Sigma - ^1\Sigma of CO has its maximum intensity at J'=11. The internuclear distance is 1.1 Ǻ. Estimate the rotational temperature.
Homework Equations
My notes don't even really define what rotational temperature is. They say that the...
Homework Statement
Use the Fourier transform directly to solve the heat equation with a convection term
u_t =ku_{xx} +\mu u_x,\quad −infty<x<\infty,\: u(x,0)=\phi(x),
assuming that u is bounded and k > 0.
Homework Equations
fourier transform
inverse fourier transform
convolution thm
The...
Homework Statement
Solve the Dirichlet problem for the heat equation
u_y=u_{xx}\quad 0<x<2\pi, \: t>0u(x,0)=\cos xu(0,t)=u(2\pi,t)=e^{-t}
Homework Equations
The Attempt at a Solution
I have no idea what to do here. It seems to me like it's a mix of the solutions we learned. I...
Homework Statement
I hate to upload the whole problem, but I am trying to evaluate an indefinite integral, and I can follow the solution until right near the end. The example says that for a point on C_R|e^{-3z}|=e^{-3y}\leq 1. I don't understand how they can say this. Below is the question...
Homework Statement
Let f(z) = \frac{1}{z^2-1}. Find Laurent Series valid for the following regions.
• 0<|z−1|<2
• 2<|z−1|<∞
• 0<|z|<1
Homework Equations
\frac{1}{1-z}=\sum^{\infty}_{n=0}z^n,\: |z|<1
f(z)=\sum^{\infty}_{n=0}a_n(z-z_0)^n+\sum^{\infty}_{n=1}b_n(z-z_0)^{-n}
The Attempt at a...
Homework Statement
I have the functionu(x,t)=\frac{1}{2c}\int^{x+ct}_{x-ct}g(\xi)d\xiwhere g is continuously differentiable and c is a constant. I need to verify that this is a solution to the wave equation.
Homework Equations
My prof gave me the...
Homework Statement
I need to write a program that takes a text file, and looks for how many unique words it has, as well as the number of times they occur in the file.
Homework Equations
None
The Attempt at a Solution
public static void main(String[] args) throws FileNotFoundException...
Homework Statement
My textbook gives me this definition of a connected set.
http://media.newschoolers.com/uploads/images/17/00/69/80/76/698076.png [Broken]
I have been working through my practice problems and I got to one that asked me to sketch the set given by|z+2-i|=2and note whether it is...
Homework Statement
I am going over a practice exam, and I need to find the FSS of f(x)=x(\pi^2-x^2)
Homework Equations
f(x) \sim \sum^\infty_{n=1}a_n sin\left(\frac{n \pi x}{L}\right)
a_n=\frac{2}{L}\int^L_0 f(x)sin\left(\frac{n\pi x}{L}\right)dx
The Attempt at a Solution
I think I...
Homework Statement
Consider the Laplace’s equation, ∆u(r,θ) = 0, inside the quarter-circle of radius 2 (0 ≤ θ < π, 0 ≤ r ≤ 2), where the boundary θ is insulated, and u(r,\theta/2)=0
Show that the insulated boundary condition can mathematically be expressed as
\frac{\partial u}{\partial...
Homework Statement
a) Show that the Fourier Cosine Series of f(x)=x,\quad 0\leq x<L is
x ~ \frac{L}{2}-\frac{4 L}{\pi ^2}\left[\left(\frac{\pi x}{L}\right)+ \frac{\cos\left(\frac{3\pi x}{L}\right)}{3^2}+\frac{\cos\left(\frac{5 \pi x}{L}\right)}{5^2}+\dots\right]
b) use the above series to...
Homework Statement
Find \sin^{-1}(-2) by writing [tex]sin w = -2[/itex] and using the rectangular representation of \sin w
Homework Equations
Rectangular representation of \sin w
The Attempt at a Solution
I think my biggest problem here is I have literally no idea what the...
Can someone please explain to me what a "dynamical trajectory" means?
I am reviewing the first chapter of my classical mechanics book (Fetter & Walecka), and in the very first section he uses the term "dynamical trajectory". I have seen this derivation many times, but I just don't understand...
Homework Statement
Assume that the center of mass of the earth moves with approximately constant velocity with respect to the fixed stars, and that \mathbf{\omega}, the angular velocity of the earth, is constant. Rederive the terrestrial equations of motion...
Homework Statement
Show that the inequality\left|\frac{z^2-2z+4}{3x+10}\right|\leq3holds for all z\in\mathbb{C} such that |z|=2
Homework Equations
Triangle inequality
The Attempt at a Solution
I'm not really sure how to go about this. the x is throwing me off. Should I write it out with...
Homework Statement
A solid conducting disk of radius a rotates about its symmetry axis with
angular speed ω rads/s. If there is a uniform magnetic field \mathbf{B} perpendicular to the disk derive an expression for the potential difference induced between the centre of the disk and its rim...
Homework Statement
I'm working through a proof that says the magnetic field of a toroid is circumferential at all points inside and outside the toroid. I can follow most of the proof, but am a bit confused where the first equation comes from.
Here is the figure from the textbook (Griffith's...
Homework Statement
If a state is a linear combination of two energy eigenstates, does its wavefunction satisfy the time independent shrodinger equation? I guess in general, how would I show if the wavefunctions of a state does or does not satisfy the time-independent schrodinger equation...
Homework Statement
https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-prn2/1483071_10151813160569290_1331827985_n.jpg
Homework Equations
\left|\psi ,t\right\rangle=\sum_i c_i(t)e^{-\frac{i E_n t}{\hbar}}\left|n\right\rangle
The Attempt at a Solution
I'm quite lost on how to even start this...
So I am trying to learn this. It is not making sense to me. Every single resource I have found tells me I need to make some weird substitution, and then it becomes a differential equation that has the Airy equation as a solution, and then skips to finding the energy eigenvalues as a function of...
Homework Statement
Show that the two-body hamiltonianH_{\text{sys}}=\frac{\mathbf{p}_1^2}{2m_1}+\frac{\mathbf{p}_2^2}{2m_2}+V( \mathbf{r}_1,\mathbf{r}_2)can be separated into centre of mass and relative...
Homework Statement
I'm trying to work through an example in my classical mechanics textbook (Fowles and Cassiday, 7th ed, example 6.7.2. The problem I am having is when he expands the integrand into a power series. I'll write out the first part of the solution. The question is "find the...
Homework Statement
I have measured the amplitude between the first and tenth oscillations for a damped harmonic oscillator (spring with a mass attached). I also have measured the period. First question. Is an (underdamped) harmonic oscillator periodic? Like I know that the solution to the...
Homework Statement
This is quite a long problem, and I have most of it figured out, but I am getting stuck on the very last part of the problem. My problem is I do not understand how to find \left\langle\psi|a_1\right\rangle in the very last line. Is...
Homework Statement
A beam of spin-1/2 particles is prepared in the state
\left|\psi\right\rangle=\frac{2}{\sqrt{13}}\left|+\right\rangle_x+i \frac{2}{\sqrt{13}}\left|-\right\rangle_x
￼￼￼￼a) What are the possible results of a measurement of the spin component Sz, and with what probabilities...
Homework Statement
A particle moving in one dimensions is in the state |\psi\rangle with position-space wave function \psi(x) = Ae^{−\lambda|x|} where A, λ are positive real constants.
a)Normalize the wavefunction.
b)Determine the expectation values of x and x^2
Homework Equations...
Homework Statement
I need to derive the intensity distribution of the double slit experiment. Intensity as a function of the slit separation d, the distance to the screen L and the wavelength \lambda. L>>d
Homework Equations
The Attempt at a Solution
Ok this is ridiculous but...
Homework Statement
So I need to identify the optical filter with jones matrix
A=\frac{1}{sqrt{2}}e^{-i\pi /4}\left[\begin{matrix}1&-i \\ -i&1 \end{matrix}\right]
Homework Equations
See attempt
The Attempt at a Solution
So I have applied the rotation matrix like this ...
Homework Statement
F(x)=\int^{2x}_1\frac{e^{xy}\cos y}{y}dy
Show that F is of class C^1, and compute the derivative F′(x).
Homework Equations
Thm:
Suppose S and T are compact subsets of \mathbb{R}^n \text{ and } \mathbb{R}^m, respectively, and S is measurable. if f(\bf{x,y}) is...
Homework Statement
Let (u,v)=\mathbf{f}(x,y,x)=(2x+y^3,xe^{5y-7z})
Compute D\mathbf{f}(x,y,z),\;\partial (u,v)/\partial(x,y),\;\partial (u,v)/\partial(y,z)\text{ and }\partial (u,v)/\partial(x,z)
Homework Equations
-chain rule
The Attempt at a Solution
well I can get...