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Quantum Mechanics
Quantum Mechanics is the branch of physics that deals with the study of the structure and behavior of atoms and molecules. It is primarily based on Max Planck's Quantum theory, which incorporates Heisenberg's uncertainly principle and the de Broglie wavelength to establish the wave-particle duality on which Schrodinger's equation is based.
916 Questions
What would happen if the direction of the current through a hall probe is reversed?
The idea is that the magnetic field of the device reacts with the external magnetic field. If the current is reversed, the magnetic field would also be reversed, and the reading would be the opposite.
What is the maximum number of electrons possible in a set of 5f orbitals?
The maximum number of electrons possible in a set of 5f orbitals is 14. Each f orbital can hold a maximum of 2 electrons, and there are a total of 7 f orbitals (l=3 for f orbitals), so the total number of electrons that can be accommodated is 7 x 2 = 14.
What technology helped scientists learn about quarks?
The quark model was independently proposed by Murray Gell-Mann and George Zweig in 1964. This was well before computers were powerful enough to analyze any data from particle accelerator collision observations (the CDC 6600 supercomputer was just introduced that year).
The devices for making these observations at the time were cloud chambers, bubble chambers, spark chambers, etc. and photographs of the trails were taken and visually analyzed by humans.
It probably was not until the late 1960s when minicomputers became widely available that data from more advanced detectors could be collected and the data disks or tapes taken to large scientific mainframes for computer analysis.
So the actual technologies used to develop the model were:
- particle accelerators - e.g. van de graaff machines, cyclotrons, synchrotrons, betatrons
- detection devices - e.g. cloud chambers, bubble chambers, spark chambers
- photography
- measurement tools - e.g. protractors, length scales
- electromechanical calculators
- etc.
How does quantum mechanics stop Newtonian determinism?
The Heisenberg Uncertainty Principle as well as wave-particle duality prevent any form of determinism at the quantum level. This is because Newtonian determinism requires the position of matter to be certain and HUP makes the position of matter uncertain and Wave-Particle Duality questions whether something has mass at all in a given location.
What does Quantum tunneling refer to?
Quantum tunneling is a physics phenomenon within the area of quantum mechanics. Basically it refers to when a particle can tunnel through a barrier that it could not surmount in classic physics.
You don't have to not have a lens to focus EM waves to an image in order to postulate that reality is made up of waves: double-slit interference experiments shows that light is made up of waves, even while the photoelectric effect shows that light is made up of discrete particles! And the neutron interferometer experiment shows that matter does behave as if it were a wave. Thus we have particles with wave nature, and waves with particle nature.
(see wave/particle duality link below for more information.)
What are some popular mechanics tools?
Some popular mechanics tools include drills, weights, screwdrivers, tension springs, hammers, nails, and screws. Popular mechanic tools often come a kit that includes all of the above and more.
Is an electron a standing wave?
No -- an electron is a point particle with mass, charge, and spin.
The probability that you will find an electron at a specific point can, however, often be calculated by wave functions.
Any moving mass can be considered either a particle or a wave. Its properties can be defined via the deBorlie wave equation.
Why the particle higgs boron has not been observed?
Three reasons:
1) Its large mass requires a LOT of kinetic energy in any collision to end up with enough energy to even possibly result in a Higgs Boson being created. That's why no particle accelerator prior to FermiLab or CERN had anywhere near enough energy to even hope to make a Higgs.
2) The Higgs is a VERY unstable particle -- once created, it breaks down into other particles in a time on the order of 10^-22 seconds. No device can possibly detect a particle in existence for that length of time, so we are left with looking for the decay products of a Higgs.
3) A LOT of other particles have decay products that very closely resemble that of the Higgs, so we can never be 100% certain that "these decay products are from Higgs Bosons, while these are not." All we can do is make a LOT of collisions, record the decay products of all of them, and then ask the question, "What is the probability that NONE of these decay products are a Higgs?" The most recent data from CERN have led scientists to state that the odds that zero Higgs were created is 1000 to 1 -- pretty good odds. However, particle science protocol requires that this probability must be reduced to a million to one before stating, "The particle that we were looking for was definitely created during these experiments." That announcement will probably occur in the next year or so.
What is the probability that Beta minus decay will occur on a given neutron in a given second?
The probability is very close to zero.
What is the purpose of the reduced Planck constant?
The reduced Planck constant simplifies the mathematics found in quantum physics calculations by adding a 2pi term into it. Instead of worrying about that 2pi constant, formulas using the reduced Plank constant have it built in.
What is the role of an observer in wave function collapse?
The question itself is controversial, as we're not sure if the observer has anything to do with the wave collapse.
However, once the ability to observe (or interact) with a given particle is enabled, the wave-function or probability wave of that particle peaks, or collapses into a finite quantity.
As said, we're not sure if a conscious observer has anything to do with it, or if it has to do with physical interactions in and of themselves.
Another opinion:
The observer has nothing to do with the collapse of the wave function. It is the measurement acting on the the wave function that does the collapsing. The part about which we are uncertain (we, as in physicists) is whether nature performs the measurement before we do and we get the result, or if nature leaves the wave function as a superposition until we measure it. This is the fundamental question of Schrodinger's cat in a box paradox.
How do you solve the time dependent Schrodinger wave equation?
If V is only a function of x, then the equation's general solution can be nearly solved using the method of separation of variables.
Starting with the time dependent Schrödinger equation:
(iℏ)∂Ψ/∂t = -(ℏ2/2m)∂2Ψ/∂x2 + VΨ, where iis the imaginary number, ℏ is Plank's constant/2π, Ψ is the wave function, m is mass, x is position, t is time, and V is the potential and is only a function of x in this case.
Now we find solutions of Ψ that are products of functions of either variable, i.e.
Ψ(x,t) = ψ(x) f(t)
Taking the first partial of Ψ in the above equation with respect to t gives:
∂Ψ/∂t = ψ df/dt
Taking the second partial of Ψ in that same equation above with respect to x gives:
∂2Ψ/∂x2 = d2ψ/dx2 f
Substituting these ordinary derivatives into the time dependent Schrödinger equation gives:
(iℏψ)df/dt = -(ℏ2/2m)d2ψ/dx2f + Vψf
Dividing through by ψf gives:
(iℏ)(1/f)df/dt = -(ℏ2/2m)(1/ψ)d2ψ/dx2 + V
This makes the left side of the equation a function of tonly, and the right a function of x only; meaning both sides have to be a constant for the equation to hold (I'm not going to prove why this is so, because if you've understood what I've written up to this point, you're probably familiar with the separation of variables technique).
That allows us to make two separate ordinary differential equations:
1) (1/f)df/dt = -(iE/ℏ)
2) -(ℏ2/2m)d2ψ/dx2 + Vψ = Eψ, where E is the constant that both separated differential equations must equal to (I did a little bit of algebra to these equations also). This is known as the time independent Schrödinger equation.
To solve 1) just multiply both sides of the equation by dt and integrate:
ln(f) = -(iEt/ℏ) + C. Exponentiating and, since C will be absorbed later, removing C:
f(t) = e-(iEt/ℏ)
Now, we have gone as far as we can until the potential, V(x), is specified. That leaves us with the general solution to the time dependent Schrödinger equation being:
Ψ(x,t) = ψ(x) e-(iEt/ℏ)
There are many solvable examples of ψ(x) for specific V(x). I've linked some below. Also, if V is a function of both x and t, there are methods to find solutions, such as perturbation theory and adiabatic approximation.
