Recent content by ausdreamer

Homework Statement If 0 <= A <= B, prove that: A(B-A) <= (B/2)^2 Homework Equations - The Attempt at a Solution I've been blindly rearranging the terms trying to see a way to prove this but due to my complete lack of experience in proofs, I'm hoping someone here can give a little...

Thanks, this helped a lot :)

Homework Statement I know how to derive the density of states for an ideal gas by using the energy equation: E_n = A*n^2, where A = (h_bar^2*pi^2)/(2mL^2) but what about for a 'photon gas'? Do I use the same energy equation as above, or the following: E_n = (h_bar*pi*c/L)*n...

Yes, but I'm required to write an uncertainty analysis and that reasoning isn't detailed enough :( I'm just looking for confirmation of my idea to carry out the standard uncertainty formula (sqrt(...)) but substitute in the lower uncertainty in A and B to find the lower uncertainty in C, and...

I mean I used a program to find the values of A and B, and it also gave me the lowest possible value and largest possible value for each. But it turns out the lower and upper values aren't equally far away from the actual result it gave for the quantity. So if you pictures the measurement of A...

Thanks for your reply DiracRules, but I don't think it has answered my question. I just want to know how to calculate the uncertainty given my uncertainty is not equal above or below the measured value. (Ie. not A=50+/-2, but a measured value of A=50 with a lower value of 48, and maximum value...

Homework Statement If I measure A=50, with a minimum value of 48, and a maximum value of 51, and measure B=100, with a minimum value of 92, and a maximum value of 115, and I add the two (C=A+B) together, what is the resulting minimum and maximum value of C? Homework Equations If A...

Homework Statement I have to evaluate the following integral: \frac{\partial \log\rho (r)}{\partial \log r} for \rho (r) = \rho_0 \Big(1+\big(\frac{r}{\alpha}\big)^2\Big)^\frac{-3 \beta}{2} where \rho_0,\alpha,\beta are constants and r is a random variable. Homework Equations...

Well the problem stated q as positive odd integers, and also my lecturer said we can ignore the 1/2h_bar * w term since all we're interested in is the difference in energy not E itself.

Homework Statement Consider a system composed of 2 harmonic oscillators with frequencies w and 2w respectively (w = omega). The total energy of the system is U=q * h_bar * w, where q is a positive negative integer, ie. q = {1, 3, 5, ...}. Write down the number of microstates of the system...

Ah I see, thanks for that lancedance :) There's more parts to this question that I might post here in case anyone sees this in the next 12 hours or so before my exam I'm studying for :)... (Continuing on from the arbitrary state |alpha>...) Suppose we make a measurement that selects only...

So we can write: cos(A) = sum_a' [(cos(A) |a'>) <a'|] = sum_a' [sum_b' [|b'><b'| (cos(A) |a'>) <a'|] ] = sum_a' [sum_b' [cos(A) <b'|a'> <a'|b'>] ] = sum_c [ c^2 * cos(A)], since <b'|a'> = <a'|b'>* = <a'|b'> = c (given in the question), since A,B hermitian? OR should I do it like this...

Homework Statement 1) The position operator x has a continuous spectrum of engenvalues {x'} with corresponding eigenkets {|x'>}. Expand this state in terms of the position eigenstates. 2) Suppose the transition amplitudes c_a',b' = <a'|b'> are known where {|b'>} are the eigenstates of a...

The horizontal field. My value lies within their given range, thank you gneill :)

Homework Statement Calculate Earth's magnetic field in Brisbane. (This was for a lab report) Homework Equations B = (8.991E-3)*I*N/R = 0.6034*I (I = current going through helmholtz coils) The Attempt at a Solution I've calculated a value of 0.278 Gauss for Earth's magnetic field...