\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...
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...
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...
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...
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...
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...
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...
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...
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...
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.
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...