Recent content by MiGUi

1. Possibly a very stupid question.

\forall x\in \mathbb{R}, x \times 0 = 0 Then Let be a, b \in \mathbb{R}, a \neq b We said before that a \times 0 = 0[/tex] and also b \times 0 = 0. So, [itex]a \times 0 = b \times 0[/tex]. If we were able to divide by 0, we will have that [itex]a = b which is a contradition with...
2. Why a stationary state decay?

What EM field? Electrostatic interaction between nucleus and electrons? MiGUi
3. Why a stationary state decay?

I've been searching the answer for the called spontaneous de-excitation or free decay. We solve Time Independent Scrödinger's Equation for particles cause we know that stationary states evolves with a well defined frequency determined by de Broglie-Einstein's relations, etc. And when we...
4. Intensity of stokes and anti-stokes lines?

If I remember well, the anti-stokes line is near absorption bands. Its gain is too low there, so it is less intense than stokes line.
5. Pauli Exclusion Priciple

Cause fermions are 'defined' with the antisymmetry condition for its wavefunction and the bosons with the symmetric one. After, the spin-statistics theorem proofs that particles with an integer spin have to obey Bose-Einstein's statistic and particles with semi-integer spin have to obey...
6. Pauli Exclusion Priciple

It can exists, but if you want to 'fill' the energy levels you need at least two.
7. What is Bose Eintein Condensate?

One of the possible clasification of the particles is according to its spins. If its spin is an integer, then we call it a 'boson' and the wavefunction that describes its behavior is symmetric. If its spin is a semi integer, then we call it a 'fermion' and its wavefunction is antisymmetric...
8. Pauli Exclusion Priciple

The Pauli Exclusion Principle says that two fermions can't be in the same individual state. If we only consider the external degrees of freedom (orbiting and so) then, for one level of energy you have only one state. This stands, at least, for hydrogenoid atoms. If you consider spin...
9. Mirrors facing eachother

If put two mirrors parallel (at about .5 meter) you have a Fabry-Perot optical resonator. If the distance is less (about .5 cm) you may have a filter. This device has its own proper frequencies so if one of them is not all reflecting (such as 99% of reflecting) the radiation only emerges from...
10. Unit of work in mechanics and thermo dynamics

Work is a kind of energy. I think that the reason to call it work is historically in the context of vapor machines. We use energy to move something that can replace men's labour such as moving a piston or something else. The first law of thermodynamics says that the balance of energy is the...
11. Superposition of two electrons

If system's hamiltonian only contains spatial coordinates (such as {x,y,z} or else) you only need one wavefunction to describe the system. But, if you consider spin, since the total state space is built as \mathcal E = \mathcal{E}_{spatial} \otimes \mathcal{E}_{spin} then, a base may be the...
12. Superposition of two electrons

Superposition principle can occur when there is not interaction between particles. I mean, if in the hamiltonian there are not mixed variables, so you can make the state space as the tensor product of the spaces of individual particles, then you can apply the superposition principle. But if you...
13. Mathematica Physics and the 'i' (mathematical term)

Complex functions are sometimes useful, but physics quantities must be real. In QM, observables are hermitian operators, so its eigenvalues are real. We use, for example, imaginary exponentials to make it easier cause it is hard to work with trigonometric functions.
14. Wave collapse. Fact or fiction?

Wave packet collapse its a theorethical result. When our system is a Hamiltonian stationary state and we measure an observable which eigenvectors are the same as the Hamiltonian. E.g. a particle in a harmonic oscillator potential, \hat H = \frac{\hat p^2}{2m} + \frac{1}{2}m \omega^2 \hat x^2...
15. Irrational digits countably infinite?

rationals are countable, but irrationals are not. Between any two numbers there are infinite irrationals, and you can't know its exact value.