Thanks for the reply, the absolute value does accomplish the trick with the slight modification that I ignored the epsilons in the exponential when I did the integrals over t, otherwise I could not get the delta functions that I know I need.
I meant that if you calculate the probability density there can't be a term that is not multiplied by an exponential function hence your derivative can't have a constant all by itself. You have a -1 all by itself in your expression for the derivative.
Homework Statement
We have the lagragian L = \frac{m}{2} \dot{x}^2 - \frac{m \omega x^2}{2} + f(t) x(t)
where f(t) = f_0 for 0 \le t \le T 0 otherwise. The only diagram that survives in the s -matrix expansion when calculating <0|S|0> is D = \int dt dt' f(t)f(t') <0|T x(t)x(t')|0>...
it is not possible to have the constant in the equation all the terms in the wave functions have the exponential, the probability density has all exponentials so will its derivative.
Anything that keeps your Lagrangian invariant under a local SU(3) transformations should work. If you think about calculating the amplitude for a process the distinction between the two signs disappears also both describe the same principal bundle.
Sign Convention
It is a sign convention. Remember that V=- \int E.dl the minus sign is place there so that when we bring a charge from infinity (where the potential is defined as 0) and place it at some point in space we arrive at some positive value for V and therefore the work we have done...
I am having trouble getting the kraus matrices(E_k)) from a unitary matrix. This task is trivial if one uses dirac notation. But supposing I was coding, I can't put in bras and kets in my code so I need a systematic way of getting kraus matrices from a unitary matrix(merely using matrices). So...
In your reference frame the rod does not have proper length. Anyways, you need to be precise by what you mean "struck the sand at once". In special relativity you will need two clocks (in your reference frame)at different positions measuring the end points at the same time.
The observer in the train is moving toward the lightning strike ahead and moving away from the lightning strike behind. This observer is not in the middle.
Simple example, I am on the Earth with a clock that has been synchronized with another clock at some common origin (second clock on a plane moving past me at 50% speed of light). If I want to know what the clock reads on the plane in my reference frame, I have to use time dilation equation.
In Quantum Computation we define a map that takes on density matrix to another. It is represented by some kraus matrices. I do not know why it has to be completely positive.
A kind of projection
Think of < \psi^{'}|\psi > as a projection onto a "co-ordinate axis which here is \psi^{'}. Just like with vectors, you can have a vector in 3 dimensions and then project onto some basis like \hat{x} . Here we are in the Hilbert space spanned by the eigenstates of the...
Independence of directions
Remember that the things that happen in the x and y directions are completely independent of each other. Thus the acceleration in the y direction( which is equivalent to applying a force in y direction) only affects whatever is happening in the y direction. The...
In Griffiths book, "Introduction to Electrodynamics" example 8.4 he calculates the angular momentum density for a set up that is a version of Feynman disk paradox. His answer for the angular momentum points in the z direction. But if we you assume that the r vector has component in the s...