It really is just easiest to think about it as "the capacity to do work". Essentially, work is measured in terms of energy (work and energy have the same units). This is because energy by itself doesn't mean much, it is in reference to what is it able to physically do that matters. For...
From how my professor was describing it it seemed like the limits wouldn't be too helpful, but yes it is a definite integral from -cosh-1(a0.5 to cosh-1(a0.5 (inverse hyperbolic cosh, not cosh^-1 )
I was wondering if I could get some pointers on how to at least start on this. In quantum mechanics we are using the WKB approximation, and we end up with a definite integral that looks like this:
∫(1 - a(cosh(x))-2)1/2 dx = ∫(1/cosh(x)) (1 - a(cosh(x))2)1/2 dx
where a is a positive constant...
I have never heard of a way to investigate this mathematically but I'm sure there is. How would you describe the surface area or volume of some 3-D surface formed by moving an enclosed area along a curved axis a certain distance? You could easily describe a torus by taking a circle and forming...
The bulk limiting factor is the ability to penetrate the sample, and in forensic applications you would be using near and mid-IR spectroscopy to achieve this. The other main question is efficiency, vibrational spectroscopy methods like this don't require labeling or staining of the biomaterial...
Does it being 0 make it a special case, or it can be any eigenvalue?
Also, if you had a mixed state, would that mean the probability of simultaneous measurement would be the product of the probabilities of finding the corresponding eigenvalue for each operator? Like if A had a 50% chance of...
Let's say you have two operators A and B such that when they act on an eigenstate they yield a measurement of an observable quantity (so they're Hermitian). A and B do not commute, so they can't be measured simultaneously. My question is this: You have a matrix representation of A and B and...
I mean convolved with. I ended up working it out, my first assumption was correct I just did the work wrong. I was wondering if anyone can take a look at my result
My first thought was simply that the Fourier transform of a sum of Gaussians functions that are displaced from the origin by different amounts would just be another sum of Gaussians:
F{G1(x) + G2(x)} = F{G1(x)} + F{G1(x)}
where a generalized shifted Gaussian is: G(x) = G0exp[-(x - x0)2 / 2σ2]...
I don't see how that can possibly be true considering the quantization of all fundamental fields at each point in space as determined by quantum field theory as well as spontaneous symmetry breaking
I know that you couldn't extract work from vacuum fluctuations without violating the laws of thermodynamics, but what if there was a gradient in the vacuum energy. If you did work on the vacuum by applying some field you could then extract this work from the gradient, but if the gradient was...
So how would you find the combined chance that in picking half the pack you end up with the A,K,Q of 1 or more suits? It seems that with 26 picks the chance would be decent, I asked on another forum and someone said they found 20.71% but didn't explain how
I've been trying how to figure out how to figure out the probability of different situations in card-choosing, and I am having trouble getting my head around how to approach this:
Let's say we have two people drawing 26 of the 52 cards in a deck. What is the probability that either team has...