Homework Statement
I need to find an expression for the gain in this circuit. I know it is an interting amplifier, because with the models we were given to look at, this one fits the inverting amlpifier. I've also constructed a simulation in a simple Java applet that I have.
My problem...
Hello all,
I'm taking my first actual quantum course this semester. I went over "briefly" some quantum mechanics Fall of 2012 in a Modern Physics course during my sophomore year, currently I'm a junior.
To get straight to the point, this course is making me miserable. I had high hopes for...
Homework Statement
I need to prove for arbitrary functions φ(x) that:
\lim_{\lambda \to 0} \int_{-\infty}^{\infty} \frac{1}{\sqrt{2 \pi} \lambda} exp\left( \frac{-x^{2}}{2 \lambda^{2}} \right) \varphi(x) dx = \varphi(0),
which, in the sense of distributions is basically the delta...
Homework Statement
We measured the time between a signal source, and it's reflection coming back through our probe after going through an open-ended coaxial cable.
My teacher told us this: the cable has a polyethylene insulator between central wire and the grounding web, which has a...
Homework Statement
Noether's theorem asserts a connection between invariance principles and conservation laws. In section 7.8 we saw that translational invariance of the Lagrangian implies conservation of total linear momentum. Here you will prove that rotational invariance of L implies...
Homework Statement
When solving a D.E. with power series, I've encountered something along the lines of:
(2 - r)^{2}g'' = -2
Homework Equations
Power Series
The Attempt at a Solution
I know I am just supposed to assume such a series exists, and work from there. But I'm really...
Homework Statement
I have the equation
f(x) = \frac{\lambda^{2}}{ax^{2}}-\frac{\gamma ab}{x}
What I am assigned to do is find a value of x at it's smallest, then approximate the value of the function when x - x(smallest) is much much greater than x(smallest).
Homework Equations
f(x) = f(0)...
Homework Statement
Compare the wavelengths of a particle when it passes a barrier of height (a) +V0 and (b) -V0 where E > |V0|. Calculate the momentum and kinetic energy for both cases.
Homework Equations
(see below)
The Attempt at a Solution
I know the wavelength changes in the...
Homework Statement
Compare the wavelengths of a particle when it passes a barrier of height (a) +V0 and (b) -V0 where E > |V0|. Calculate the momentum and kinetic energy for both cases.
Homework Equations
(see below)
The Attempt at a Solution
I know the wavelength changes in the...
Homework Statement
Find absolute maxima and minima of the function in the given region:
T(x,y) = x2 + xy + y2 - 6x
Region: Rectangular plate given by: 0 ≤ x ≤ 5, -3 ≤ y ≤ 3
Homework Equations
First derivative test, fx =0, fy = 0
Second derivative test, fxxfyy - fxy2 = ?
The...
I'm required to diagonalize a 5x5 matrix by hand, using 'appropriate similarity transformations.' I'm not asking for an answer to a homework question, I'm asking is there any sort of easier (by hand) way of doing this than how I'm approaching it?
If it matters, the matrix is as follows:
A= {...
Homework Statement
Solve for x: Ax = y.
A = {{2 0 1},
{1 1 4},
{2 2 1}}
y = {{1},
{1},
{1}}
Homework Equations
Basic Matrix operations
_________________________
I have a vague idea how I'm supposed to do this, but I have no attempt yet.. eigenvalues and eigenvectors come...
Homework Statement
Find the gradient of the function at the given point. Then sketch the gradient together with the level curve that passes through the point.
g(x,y) = x2/2 - y2/2; (√2, 1)
Homework Equations
∇f = (∂f/∂x)i + (∂f/∂y)j
The Attempt at a Solution
∇g = <x, -y>
∇g(√2, 1) = <√2...
Homework Statement
Find a system K' in which the following events in frame K appear at the same time:
i) x1 = a; t1 = (2a) / c; y1 = 0; z1 = 0
ii) x2 = 2a; t2 = (3a) / (2c); y2 = 0; z2 = 0
Describe the motion of K'.
Homework Equations
Lorentz transformations; time dilation...
Homework Statement
Evaluate the following expression:
\sum_{j}\sum_{k}\epsilon_{ijk}\delta_{jk}
Homework Equations
\delta_{ij} = [i = j]
The Attempt at a Solution
I don't have a solution attempt to this one yet, because somehow I completely missed out on what the permutation thing has to do...
Homework Statement
Evaluate the following expression:
\sum_{j}\sum_{k}\epsilon_{ijk}\delta_{jk}
Homework Equations
\delta_{ij} = [i = j]
The Attempt at a Solution
I don't have a solution attempt to this one yet, because somehow I completely missed out on what the permutation thing...