Recent content by knowlewj01

edit: changed the matrix to the correct form

Homework Statement The hamiltonian for a given interaction is H=-\frac{\hbar \omega}{2} \hat{\sigma_y} where \sigma_y = \left( \begin{array}{cc} 0 & i \\ -i & 0 \end{array} \right) the pauli Y matrix Homework EquationsThe Attempt at a Solution So from the time dependent Schrödinger...

I'm also interested in this proof. if i start out with f(a)=\int_{-\infty}^{\infty}f(x)\delta(a-x) dx [1] and make the change of variable x\rightarrow -t \Rightarrow dx\rightarrow -dt then f(a)=-\int_{-\infty}^{\infty}f(-t)\delta(a+t)dt [2] i'm a bit confused how...

Homework Statement Evaluate the integral I_1 = \int_0^{2\pi} \frac{d\theta}{(5-3sin\theta)^2} Homework Equations The Attempt at a Solution I start off by switching the sine term for a complex exponential e^{i\theta}=cos\theta +isin\theta I will consider only the Imaginary...

Thanks for the replies. Is this because the function is even in the upper half of the complex plane? I thought of doing this by integrating a contour in only the positive quadrent, ie: (0,0) to (R,0) (R,0) to (0,iR) along contour ω [a radial path of radius R from the real axis to the...

Homework Statement evaluate the integral: I_1 =\int_0^\infty \frac{dx}{x^2 + 1} by integrating around a semicircle in the upper half of the complex plane. Homework Equations The Attempt at a Solution first i exchange the real vaiable x with a complex variable z & factorize...

Sorry, I don't think this was very clear. I have done some more reading: My likelihood function L(λ) is poissonian: f(k;\lambda)=\frac{e^{-\lambda}\lambda^k}{k!} Log Likelihood function is: L(\lambda)=ln\left(\Pi_{i}^{n} f(k_i;\lambda)\right) Heres where i get a bit lost, I think my...

Homework Statement I have a set of data from the DAMA experiment in which a detector attempted to measure collisions with 'WIMP's [Weakly Interacting Massive Particles] as a candidate for dark matter. The detector records the time in days of a collision event. After binning the data and...

Homework Statement an operator for a system is given by \hat{H}_0 = \frac{\hbar \omega}{2}\left[\left|1\right\rangle\left\langle1\right| - \left|0\right\rangle\left\langle0\right|\right] find the eigenvalues and eigenstates Homework Equations The Attempt at a Solution so i...

ive just noticed i made a typo in the question A = A_0e^{i\omega_r - ikz} should read A = A_0e^{i\omega_rt - ikz} so there should be a time dependance. sorry

x=x_0 e^{i\omega t - ikz} \hat{x} is the general form of a plane wave, this would propagate in the z direction with constant amplitude. correct? so initially the wavevector is complex, k = kr - i ki when the wavevector is only real, such that k = kr x_i = x_0e^{i\omega t - (ik_r + k_i)z} x_f...

The simplest waveform i can think of that has constant amplitude is x = x_0 cos(\omega t) but wouldn't a decay indicate behaviour more like x = x_0 e^{-\frac{t}{\tau}}cos(\omega t) but then how does the wavenumber come into it?

Homework Statement A wave is driven at z=0 with constant real frequency ωr propagates in the z direction, for z>0 the amplitude varies as: A = A_0 e^{i\omega_r - ikz} where k is complex k=k_r - i k_i if a wave with spatially constant amplitude and purely real wavenumber kr were...

If i were to make the substitution: \phi = \frac{2\pi x}{L} \frac{\phi}{x} = \frac{2\pi}{L} does this imply that the limits of integration change from L to 2π ?

Homework Statement An electron is confined to a 1 dimensional infinite well 0 \leq x \leq L Use lowest order pertubation theory to determine the shift in the second level due to a pertubation V(x) = -V_0 \frac{x}{L} where Vo is small (0.1eV). Homework Equations [1] E_n \approx...