The Ultimate Draft - Congrats Edgar: Team Voted Best Overall

[Redz]

SSfan is up

BASKETBALL JONES

http://www.youtube.com/watch?v=JIbp5C-5WXM

Soo, it`s my turn, right?

yup

sorry...missed ssf's pick

[Redz]

OK< Casperian disappeareed...Sorry for the confusion.  SSfan's pick was buried in Mr. T debate mania.

Skipping Bass, Evantime34, & CFF...Pretty much if anyone has missed a couple of rounds they can catch back up if they're so inclined, but I'm going to skip past them w/oo delay at this point.

wdleehi's up

I have school this weekend and will only be available sporadically.

[Casperian]

Ok, Basketball Jones was a nice try, but not the best pick here.  

Gentlemen, let me introduce to you, one of the biggest steals of the Ultimate Draft:

Ethan "Bubblegum" Tate, Cartoon Character



"Pitiful ballplayers of Earth, I am Ethan "Bubblegum" Tate, commander of the Harlem Globetrotters. For generations, your puny planet has lived in peace with the Globetrotter Homeworld. But now, for no reason, we challenge you to defend your honor on the basketball court."
―Bubblegum Tate

http://www.youtube.com/watch?v=3NYfZ1JLMiM


Why pick Michael Jordan, when you can have the GOAT of the future?
Ethan "Bubblegum" Tate is leader of the Harlem Globetrotters, the finest minds (and best basketball players) in the universe, and ruler of the Globetrotters Homeworld.
And "Bubblegum" has to be the best nickname for a basketballer ever.

Cartoon Character: Ethan "Bubblegum" Tate
Actor: Chuck Norris
Government Leader: Julius Caesar
Athlete: Charles Barkley
Villain: Lucifer
Fictional Character:
Scientist: Kurt Gödel
Super Hero:
Musician: Conan O´Brien
Wild Card: Red Auerbach

[Casperian]

OK< Casperian disappeareed...Sorry for the confusion. 

No problemo, I´ve had my post ready for over 30 minutes, but had to answer a phone-call.

[wdleehi]

Since I did well in Quantum Mechanics,

I select Erwin Schrödinger

Derivation

[edit] Short heuristic derivation

[edit] Assumptions

    (1) The total energy E of a particle is

        E = T + V = \frac{p^2}{2m}+V

            This is the classical expression for a particle with mass m where the total energy E is the sum of the kinetic energy, T = \frac{p^2}{2m}, and the potential energy V. The momentum of the particle is p, or mass times velocity. The potential energy is assumed to vary with position, and possibly time as well.

    Note that the energy E and momentum p appear in the following two relations:

    (2) Einstein's light quanta hypothesis of 1905, which asserts that the energy E of a photon is proportional to the frequency f of the corresponding electromagnetic wave:

        E = h f = {h \over 2\pi} (2\pi f) = \hbar \omega \;

            where the frequency f of the quanta of radiation (photons) are related by Planck's constant h,
            and \omega = 2\pi f\; is the angular frequency of the wave.

    (3) The de Broglie hypothesis of 1924, which states that any particle can be associated with a wave, represented mathematically by a wavefunction Ψ, and that the momentum p of the particle is related to the wavelength λ of the associated wave by:

        p = { h \over \lambda } = { h \over 2\pi } {2\pi \over \lambda} = \hbar k\;

            where \lambda\, is the wavelength and k = 2\pi / \lambda\; is the wavenumber of the wave.

    Expressing p and k as vectors, we have

        \mathbf{p} =\hbar \mathbf{k}\;

[edit] Expressing the wave function as a complex plane wave

Schrödinger's great insight, late in 1925, was to express the phase of a plane wave as a complex phase factor:

        \Psi(\mathbf{x},t) = Ae^{i(\mathbf{k}\cdot\mathbf{x}- \omega t)}

and to realize that since

        \frac{\partial}{\partial t} \Psi = -i\omega \Psi

then

        E \Psi = \hbar \omega \Psi = i\hbar\frac{\partial}{\partial t} \Psi

and similarly since

        \frac{\partial}{\partial x} \Psi = i k_x \Psi

and

        \frac{\partial^2}{\partial x^2} \Psi = - k_x^2 \Psi

we find:

        p_x^2 \Psi = (\hbar k_x)^2 \Psi = -\hbar^2\frac{\partial^2}{\partial x^2} \Psi

so that, again for a plane wave, he obtained:

        p^2 \Psi = (p_x^2 + p_y^2 + p_z^2) \Psi = -\hbar^2\left(\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2}\right) \Psi = -\hbar^2\nabla^2 \Psi

And by inserting these expressions for the energy and momentum into the classical formula we started with we get Schrödinger's famed equation for a single particle in the 3-dimensional case in the presence of a potential V:

        i\hbar\frac{\partial}{\partial t}\Psi=-\frac{\hbar^2}{2m}\nabla^2\Psi + V\Psi

[edit] Longer discussion

The particle is described by a wave; the frequency is the energy E of the particle, while the momentum p is the wavenumber k. Because of special relativity, these are not two separate assumptions.

        E= \hbar \omega \;\;\;\;p=\hbar k \,

The total energy is the same function of momentum and position as in classical mechanics:

            E = T(p) + V(x) = {p^2\over 2m} + V(x)

where the first term T(p) is the kinetic energy and the second term V(x) is the potential energy.

Schrödinger required that a Wave packet at position x with wavenumber k will move along the trajectory determined by Newton's laws in the limit that the wavelength is small.

Consider first the case without a potential, V=0.

        E = {1\over 2m} (p_x^2+p_y^2 + p_z^2)
        \omega = {\hbar\over 2m} (k_x^2 + k_y^2 + k_z^2)

So that a plane wave with the right energy/frequency relationship obeys the free Schrödinger equation:

        i \hbar {\partial \over \partial t} \Psi = -{\hbar^2 \over 2m} \left( {\partial^2 \Psi \over \partial x^2} + {\partial^2 \Psi \over \partial y^2} + {\partial^2 \Psi \over \partial z^2} \right)

and by adding together plane waves, you can make an arbitrary wave.

When there is no potential, a wavepacket should travel in a straight line at the classical velocity. The velocity v of a wavepacket is:

        v = {\partial \omega \over \partial k } = {\partial \over \partial k} { k^2\over 2m} = { k\over m}

which is the momentum over the mass as it should be. This is one of Hamilton's equations from mechanics:

        {dx \over dt} = {\partial H \over \partial p}

after identifying the energy and momentum of a wavepacket as the frequency and wavenumber.

To include a potential energy, consider that as a particle moves the energy is conserved, so that for a wavepacket with approximate wavenumber k at approximate position x the quantity

        {\hbar^2 k^2\over 2m } + V(x)

must be constant. The frequency doesn't change as a wave moves, but the wavenumber does. So where there is a potential energy, it must add in the same way:

        i\hbar {\partial \over \partial t}\Psi=-{\hbar^2 \over 2m}\nabla^2\Psi + V(x)\Psi

This is the time dependent Schrödinger equation. It is the equation for the energy in classical mechanics, turned into a differential equation by substituting:

        E\rightarrow i\hbar {\partial\over \partial t} \;\;\;\;\;\; p\rightarrow -i\hbar {\partial\over \partial x}

Schrödinger studied the standing wave solutions, since these were the energy levels. Standing waves have a complicated dependence on space, but vary in time in a simple way:

        \Psi(x,t) = \psi(x) e^{- iEt / \hbar } \,

substituting, the time-dependent equation becomes the standing wave equation:

        {E}\psi(x) = - {\hbar^2 \over 2m} \nabla^2 \psi(x) + V(x) \psi(x)

Which is the original time-independent Schrödinger equation.

In a potential gradient, the k-vector of a short-wavelength wave must vary from point to point, to keep the total energy constant. Sheets perpendicular to the k-vector are the wavefronts, and they gradually change direction, because the wavelength is not everywhere the same. A wavepacket follows the shifting wavefronts with the classical velocity, with the acceleration equal to the force divided by the mass.

An easy modern way to verify that Newton's second law holds for wavepackets is to take the Fourier transform of the time dependent Schrödinger equation. For an arbitrary polynomial potential this is called the Schrödinger equation in the momentum representation:

            i\hbar {\partial \Psi(p,\,t) \over \partial t} = {p^2\over 2m} \Psi(p,\,t) + V(i{\partial\over \partial p}) \Psi(p,\,t)

The group-velocity relation for the fourier transformed wave-packet gives the second of Hamilton's equations.

            {dp \over dt} = -{\partial H \over \partial x}

wdleehi
Cartoon Character: C. Montgomery Burns
Actor:  Andre the Giant
Government Leader:
Athlete:  Magnus Samuelsson
Villain:  Megatron
Fictional Character:  Harry Potter
Scientist:  Erwin Schrödinger
Super Hero: Silver age Superman
Musician:  Rick James
Wild Card: Mr. Mxyzptlk

[Redz]

Mgent's up

[Redz]

celticinorlando's up

[fairweatherfan]

Arent u getting 5 for one with voltron
If so wich voltron??
the lion one
the cars one
the plane one
??


If so I demmand to include pinki in my brain pick....

 

The Voltron is the only true Voltron, the lion version.  I asked for a ruling on it when I made the pick and I guess it was allowed.  I'm only taking the robot, not the pilots though, so I think it's ok as one individual.

[Redz]

Arent u getting 5 for one with voltron
If so wich voltron??
the lion one
the cars one
the plane one
??


If so I demmand to include pinki in my brain pick....

 

The Voltron is the only true Voltron, the lion version.  I asked for a ruling on it when I made the pick and I guess it was allowed.  I'm only taking the robot, not the pilots though, so I think it's ok as one individual.

I, as a mere mortal, non-comic lover, feel incapable of ruling in this scenario.

I'll let you guys duke it out!

Off to class I go...

[celticinorlando]

I select my villian, Bill Laimbeer



Cartoon Character: Michael Jordan
Actor:  Wilt Chamberlain
Government Leader: Barrack Obama
Athlete:  Tim Duncan
Villain:  Bill Laimbeer
Fictional Character:  Jimmy Chitwood
Scientist:  Dr. James Naismith
Super Hero: The Flash
Musician:  
Wild Card: Jackie Moon

[SSFan 6.33]

I select my villian, Bill Laimbeer



Cartoon Character: Michael Jordan
Actor:  Wilt Chamberlain
Government Leader: Barrack Obama
Athlete:  Tim Duncan
Villain:  Bill Laimbeer
Fictional Character:  Jimmy Chitwood
Scientist:  Dr. James Naismith
Super Hero: The Flash
Musician:  
Wild Card: Jackie Moon

you evil villainous bahstahd!!   

[indeedproceed]

I select my villian, Bill Laimbeer



Cartoon Character: Michael Jordan
Actor:  Wilt Chamberlain
Government Leader: Barrack Obama
Athlete:  Tim Duncan
Villain:  Bill Laimbeer
Fictional Character:  Jimmy Chitwood
Scientist:  Dr. James Naismith
Super Hero: The Flash
Musician:  
Wild Card: Jackie Moon

OHHH I Hate that guy!

[celticinorlando]

indeed..i can think of no other person i would rather punch in the face than bill laimbeer

[SSFan 6.33]

indeed..i can think of no other person i would rather punch in the face than bill laimbeer

Chief!!

[wdleehi]

Some quick news from my team.

Schrödinger, Megatron and Mr. Mxyzptlk have gotten together and finally created that cat box.


Unfortunately they couldn't find any cats.  Therefor, with the help of Superman, they have been rounding up Voltron lions to use in their experiments.


Mr. Mxyzptlk reports when the Lions are in the box, they are indeed both dead and alive (being a 5th dimensional elf has allowed him to see into the box)

Sadly, it is also being reported when the box is open, the live lion ceases to exist.