Intuitively, I aggree with dipole's opinion. Since you want to describe an elastic collision, adjust the parameters of the sharp function that you chosed, so that the Hamiltonian and the momentum have vanishing Poisson brackets.
I took the wikipedia's definition of Minkowski space: a 4-D real vector space with a symmetric, bilinear, non-degenerate quadratic form with signature (1,3). From this point of view, can a consistent metric induced by that quadratic form? If not, then according to your comment, I will have to...
How "continuity" of a map Τ:M→M, where M is a Minkowski space, can be defined? Obviously I cannot use the "metric" induced by the minkowskian product:
x\cdoty = -x^{0}y^{0}+x^{i}y^{i}
for the definition of coninuity; it is a misinformer about the proximity of points. Should I use the Euclidean...
So, that would be true if the function:
1\cdot : V→V , 1\cdot:X→1\cdotX
is surjective? But this is an extra axiom, more complicated than it's substitute (that is (2)). Better keep (2) as it is... :smile:
Thank's for your replies!
Hello, I'd like to make a, probably stupid, question regarding the axioms that define a vetor space. Among them, there are the axioms:
λ\cdot(μ\cdotX) = (λμ)\cdotΧ (1) and 1\cdotΧ=Χ (2)
for all λ,μ in the field and for all X in the vector space, where 1 is the identity of the...
Would you mind if I decribe you my attempt to find some potentials? As it looks so far, I have managed to find some potentials that represent the fields (where the connection between fields and the potentials is more compicated then the usual one) and also I managed to find the gauge...
What means that a function is an eigen-function of some operator? Doesn't this mean that when you act with that operator on that function, the result will be the original function multiplied by a constant (where this constant is the eigenvalue)?
So, try to operate with HQHO on u(q) and see what...
@Vanhess71
I understand that in order to explain the charge quantization, one has to assume the existence of magnetic monopoles. But my concern is not why should there be some magnetic charge. What I want to do is to axiomaticaly accept the existence of magnetic sources (i.e. the existence of a...
Homework Statement
This is not actually a homework but a personal work. Here it is:
Using the differential forms:
F=\tfrac{1}{2!}{{F}_{\mu \nu }}d{{x}^{\mu }}\wedge d{{x}^{\nu }} and J=\tfrac{1}{3!}{{J}^{\mu }}{{\varepsilon }_{\mu \alpha \beta \gamma }}d{{x}^{\alpha }}\wedge d{{x}^{\beta...
In Newtonian theory it affects EVERYTHING which has the property of "mass". In GR theory it affects EVERYTHING, since it apperars in the equations of motion (geodesic equations). So, yes, according to us so far understanding of gravity, gravity affects everything, reagrdless its space scale.
Why don't you try to express en and et in terms of ex and ey ? Doing that, you can find the total acceleration, a = an + an , in terms of its projections on x and y axis.
* e i is the unit vector in the direction of the subscript "i".
Sorry, but I can't acces to the papers at the links. Can I find them somewhere else, for free?
And something else: as I deduced from the titles, these papers seemed to refer to the subject at quantum level. If correct, is there somehting in classical level?
I think that if there was such a force, then the definition of "force", i.e. F = \dot{p} woulld be inconsistent, since the magnitude that defines the force (\dot{p}) would be in what we want to define (F) . To me, it looks non-sence to define "something" using terms that invlolve that "something".
Hello! I am trying to construct (if it is possible) a potential formulation of an electromagnetic theory which permits the presence of magnetic sources, using as a starting point the equations referred here:
http://en.wikipedia.org/wiki/Magnetic_monopole
Although I think that I have make some...
"u" is energy density, right? So, for a given volume ΔV you can find the energy content of it, using the relation ΔE = u ΔV. Ok, so far?
If yes, then consider a given surface ΔA and try to find the energy passed through it for some time interval Δt. That amount of energy, after leaving the...
This holds if the disk's center is at the origin, at z=0. But this disk is at z = a , so in your equation make the substitution z → z-a . I think that the rest are correct...
I made a mistake... This is the system:
\begin{align}
& {{\Omega }_{0}}{{c}_{i2}}={{\omega }_{i}}{{c}_{i0}} \\
& {{\Omega }_{1}}{{c}_{i2}}={{\omega }_{i}}{{c}_{i1}} \\
& {{\Omega }_{0}}{{c}_{i0}}+{{\Omega }_{1}}{{c}_{i1}}={{\omega }_{i}}{{c}_{i2}} \\
\end{align}
Now, setting...
Start with this:
Consider this linear combination:
\left| {{\psi }_{i}} \right\rangle ={{c}_{i0}}\left| 0 \right\rangle +{{c}_{i1}}\left| 1 \right\rangle +{{c}_{i2}}\left| 2 \right\rangle
These superpositions will be eigenstates if:
{{H}_{I}}\left| {{\psi }_{i}} \right\rangle...
Since the hamiltonian consists of the states |0> , |1> and |2> , these will be a basis for it's non-zero eigenvalue eigenstates, because, if you acted with the hamiltonian to every other state |n>, you will get zero (assuming that |n>'s are a complete set of orthonormal states). So, try to act...
OK, first a correction. EMF is not created only by electrons, but by every kind of particle that has the fundamental property of "electric charge". There are many kinds of such elementary particles: electron, muon, tau, quarks, W bosons and their antiparticles (what you call "negative...
Let me give you an alternative way to derive the current's expression, which maybe has more sense. What we are looking for is a function that satisfies the “continuity equation”:
{{\partial }_{t}}\rho +{{\partial }_{x}}j=0
which comes from the requirement of local conservation of probability...
"What is spin?" is a question of the species "What mass, charge, or color is?" and the answer is the same: "A fundamental property of elementary particles". I think that this property had been observed for the fist time in the famous "Stern–Gerlach experiment" or, according to wikipedia, "in the...
Coulomb's law for a point charge in the origin is:
\mathbf{E}\left( \mathbf{r} \right)=\frac{q}{4\pi {{\varepsilon }_{0}}}\frac{{\mathbf{\hat{r}}}}{{{r}^{2}}}
When you integrate the field on an arbitrary closed surface (that includes the origin):
\oint\limits_{S}{\mathbf{E}\cdot...
Take a look at this for part b) (which also answers a) ). I combine the equations:
dm=adx\Rightarrow \dot{m}=av and \frac{d}{dt}\left( mv \right)=g\sin \varphi
to get the separable differential equation:
m\dot{v}+a{{v}^{2}}=g\sin \varphi
which is solved as:
\begin{align}...
Almost... To show that a state is an eigenstate of some operator, all you have to do is to show that when that operator acts on that state, gives the same state multiplied by some constant (like the last of the equalities I presented). In general, U|jm> does not have to be equal to |j,-m>, since...
It's pretty simple and doesn't need futher arguing:
Force = f(v) (function of velocity, where the functional form depends on shape)
Power loss = f(v)\cdotv (equall for both ships)
To keep velocity or kinetic energy constant, you have to give energy at the same rate of losing it. But...
Of course, this is an exactly solvable problem and we have the tools to do it. Polls are needed when there is not an objective answer, which of course is not the case of this problem.
I agree... The force depends on the velocity and shape, so they are the same, and since the spaceships are co-traveling, they lose energy with the same rate since:
Power = f v = rate of energy loss
Your brother is partly right, since more mass means less deceleration, but also more mass means...
You have to use the equation:
U\left[ {{R}_{1}}\left( \pi \right) \right]{{J}_{3}}{{U}^{-1}}\left[ {{R}_{1}}\left( \pi \right) \right]=-{{J}_{3}}
which comes from the transformation law of the rotation generators:
U\left( R \right){{J}^{ij}}{{U}^{-1}}\left( R...
That will not solve anything... The formula for the momentum has to be used. I recommend you to start with "p = γmv" and find "v" as a function of "p", then find "γ" as a function of "p" and finaly replace "γ" in "E=γmc2" with what you have found.
Sorry, I have misread the question. You should find the time needed for the shoe to touch the ground, solving the equation h = 1/2 g Δt2 for Δt. Thren subtract it from 3.8s...
I guess it can be done that way, althought I had something else in mind:
\frac{dE}{dt}=0\Rightarrow \frac{dT}{dt}+\frac{dV}{dt}=0\Rightarrow \frac{dT}{dt}+\frac{\partial V}{\partial {{x}_{1}}}{{v}_{1}}+\frac{\partial V}{\partial {{x}_{2}}}{{v}_{2}}=0\Rightarrow
\Rightarrow...
Revise c) (Δx = 1/2 g Δt2 and include the displacement during deceleration) I found 48.4 m
About d), what is the height of the tower? Use the formula v = √(2gh)
About e), the fall lasts 2.6s+1.2s = 3.8s. Find shoe's displacement fot that time and subtract it from the height.
When we say tha energy is conserved, we mean that is constant as time passes. So the derivative of energy w.r.t. time will be zero. Althought V depends explicitly on x = x1-x2, since x1 and x2 are functions of time, then V is actually a function of time. So try to differntiate T+V=E w.r.t. time...
No, you don’t call the half-integer eigenstates “spin” and the others “angular momentum eigenstates” (<- the correct term is “orbital angular momentum”, but this is not the problem here). Since all of them are eigenstates of some angular momentum operator (which in algebraic theory of angular...
I understand that this is too much information and maybe it is quite ambiguous to you about how to use it to get results. When you clear these up, if you would like, I could guide you in some examples on how to use them.