# Search results

1. ### Simple Op-Amp Inverting Amplifier

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...
2. ### Recommendations for Study Materials [QM]

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...
3. ### Proving that the Dirac Delta is the limit of Gaussians

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...
4. ### Expectation Values - Quantum

Homework Statement \Psi (x) = C e^{i k_{0} x} e^{\frac{-x^{2}}{2 a^{2}}} Find \left\langle x \right\rangle, \left\langle x^{2} \right\rangle, \left\langle p \right\rangle, \left\langle p^{2} \right\rangle. Homework Equations Operators make a "psi-sandwich": \left\langle x \right\rangle =...
5. ### Length of coaxial cable, based on signal reflection

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...
6. ### Prove rotational invariance leads to conservation of ang. momentum

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...
7. ### Power Series to solve Second order Differential Equations

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...
8. ### Help with Maclaurin series of (1/x), (1/x^2), etc

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)...
9. ### Wavelength of Particle Passing Through Potential Barriers

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...
10. ### Wavelengths of Particle passing Potential Barriers

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...
11. ### Extrema of two-variable function in bounded region

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...
12. ### Diagonolizing 5x5 Matrix by Hand

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= {...
13. ### Solve equation Ax = y, where A and y are known

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...
14. ### Simple Gradient Question (funtion of two variables)

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...
15. ### [Special Relativity] Find frame K' in which events in K appear to be simultaneous

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...
16. ### Evaluate expression with permutaion symbol and Kronecker delta

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...
17. ### Evaluating expression involving permutation symbol and Kronecker delta

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...