when she asked us the cats name...and i said schroedinger, as its schoedinger's cat. she didnt get it.

I dont get it?

I dont get it?

because its schroedingers cat!

I think you may have just condemned yourself as a geek by posting this thread!

Yup- full geek status. Small compensation that I got the joke, but I got it none the less.

i dont get it eitha but leave da poor guy alone pmsl

I think you may have just condemned yourself as a geek by posting this thread!
me and my GF were just saying the same...she knew what it was, but its a bit more involved than a box and a dead cat...and we struggled with it.

bah, back to my airfix model making and chess for me!:thumbsup:

Yup- full geek status. Small compensation that I got the joke, but I got it none the less.
we rescued the cat not long ago, and named it splodge (it was blackie by previous owner) but watching the big bang theory (comedy programme) it seemed such a cool name. makes us look smart! (and for those on here that have met me, you know it aint true!!) hehe

hope this explains it all :loopy:


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

The solution \Psi(x,\,t) for any initial condition ψ0(x) can be found by Fourier transforms. Because the coefficients are constant, an initial plane wave stays a plane wave. Only the coefficient changes:

\Psi(x,\,t) = A(t) e^{i k x} \,

Substituting:

{dA(t) \over dt} = -{i\hbar k^2 \over 2m} A(t) \,

So that A is also oscillating in time:

A(t) = A e^{- i \hbar{k^2 \over 2m} t} \,

and the solution is:

\Psi(x,\,t) = A e^{i k x - i \omega t} \,

Where \omega=\hbar k^2/2m, a restatement of DeBroglie's relations.

To find the general solution, write the initial condition as a sum of plane waves by taking its Fourier transform:

\psi_0(x) = \int_k \psi(k) e^{ikx} \,

The equation is linear, so each plane waves evolves independently:

\Psi(x,\,t) = \int_k \psi(k)e^{-i\omega t} e^{ikx} \,

Which is the general solution. When complemented by an effective method for taking Fourier transforms, it becomes an efficient algorithm for finding the wavefunction at any future time--- Fourier transform the initial conditions, multiply by a phase, and transform back.

[edit] Gaussian wavepacket

An easy and instructive example is the Gaussian wavepacket:

\psi_0(x) = e^{-x^2 / 2a} \,

where a is a positive real number, the square of the width of the wavepacket. The total normalization of this wavefunction is:

\langle \psi|\psi\rangle = \int_x \psi^* \psi = \sqrt{\pi a}

The Fourier transform is a Gaussian again in terms of the wavenumber k:

\psi_0(k) = (2\pi a)^{d/2} e^{- a k^2/2} \,

With the physics convention which puts the factors of 2π in Fourier transforms in the k-measure.

\psi_0(x) = \int_k \psi_0(k) e^{-ikx} = \int {d^dk \over (2\pi)^d} \psi_0(k) e^{-ikx}

Each separate wave only phase-rotates in time, so that the time dependent Fourier-transformed solution is:

\psi_t(k) = (2\pi a)^{d/2} e^{- a { k^2\over 2} - it {k^2\over 2m}} = (2\pi a)^{d/2} e^{-(a+it/m){k^2\over 2}} \,

The inverse Fourier transform is still a Gaussian, but the parameter a has become complex, and there is an overall normalization factor.

\psi_t(x) = \left({a \over a + i t/m}\right)^{d/2} e^{- {x^2\over 2(a + i t/m)} } \,

The branch of the square root is determined by continuity in time--- it is the value which is nearest to the positive square root of a. It is convenient to rescale time to absorb m, replacing t/m by t.

The integral of ψ over all space is invariant, because it is the inner product of ψ with the state of zero energy, which is a wave with infinite wavelength, a constant function of space. For any energy state, with wavefunction η(x), the inner product:

\langle \eta | \psi \rangle = \int_x \eta(x) \psi_t(x),

only changes in time in a simple way: its phase rotates with a frequency determined by the energy of η. When η has zero energy, like the infinite wavelength wave, it doesn't change at all.

The sum of the absolute square of ψ is also invariant, which is a statement of the conservation of probability. Explicitly in one dimension:

|\psi|^2 = \psi\psi^* = {a \over \sqrt{a^2+t^2} } e^{-{x^2 a \over a^2 + t^2}}

Which gives the norm:

\int |\psi|^2 = \sqrt{\pi a}

which has preserved its value, as it must.

The width of the Gaussian is the interesting quantity, and it can be read off from the form of | ψ2 | :

\sqrt{a^2 + t^2 \over a} \,.

The width eventually grows linearly in time, as \scriptstyle t/\sqrt{a}. This is wave-packet spreading--- no matter how narrow the initial wavefunction, a Schrödinger wave eventually fills all of space. The linear growth is a reflection of the momentum uncertainty--- the wavepacket is confined to a narrow width \scriptstyle \sqrt{a} and so has a momentum which is uncertain by the reciprocal amount \scriptstyle 1/\sqrt{a}, a spread in velocity of \scriptstyle 1/m\sqrt{a}, and therefore in the future position by \scriptstyle t/m\sqrt{a}, where the factor of m has been restored by undoing the earlier rescaling of time.

As my grandmother would say, 'and merry Christmas to you too!'.

http://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat

that explains it all...

You geek!!

*hides her t-shirt that says "Schrödinger's cat is not dead" on one side and "Schrödinger's cat is dead" on the other. :blush:

Edit: I think you'll like this site... http://www.thinkgeek.com/tshirts-apparel/womens/6f59/ *whistles*:P

They do it in unisex too of course!

You geek!!

*hides her t-shirt that says "Schrödinger's cat is not dead" on one side and "Schrödinger's cat is dead" on the other. :blush:

Edit: I think you'll like this site... http://www.thinkgeek.com/tshirts-apparel/womens/6f59/ *whistles*:P

They do it in unisex too of course!
cool...we want 2!

the big bang theory is one of the best no comides if your nerdy.

Oooooh! Now I want all of the fluffy microbes. Who wouldn't want a fluffy stachybotris?

Oooooh! Now I want all of the fluffy microbes. Who wouldn't want a fluffy stachybotris?

Errrr.... :hihi:

Edit - watch the import tax if you order from there, it's hit and miss, but if you do end up paying, it can cost more than the goods, I learnt the hard way :(

I planned to get a new cat and dog when I lost Old dog, and Jazzy cat (when his time comes), and I wanted to call the DOG Schroedinger and the CAT Pavlov (Just to be contrary!)

I planned to get a new cat and dog when I lost Old dog, and Jazzy cat (when his time comes), and I wanted to call the DOG Schroedinger and the CAT Pavlov (Just to be contrary!)

now thats just being daft.....hehe

Jules - I luv ya!! You may be a geek but at least you've rung up for a voucher. Good for you and good for Cats Protection North Sheffield branch.
Any other geeks out there, get phoning up for those vouchers!!
Sorry I cannot participate in the original thread - no idea what you're talking about, but hey I rarely do!! xx

Jules - I luv ya!! You may be a geek but at least you've rung up for a voucher. Good for you and good for Cats Protection North Sheffield branch.
Any other geeks out there, get phoning up for those vouchers!!
Sorry I cannot participate in the original thread - no idea what you're talking about, but hey I rarely do!! xx
yes, when i foned i dont think many left and for us its awkard to get to that vets, but want the cat done at all cost.
take a look here....look at the foto and dont bother reading the rest...we tried and fell asleep!:thumbsup:
http://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat

Jules mate, WTF???

I hope CP get more vouchers or more vets participating cos it's only the first week in March and the offer has weeks to run yet. Really good that people have asked for them though. And good for you Jules for getting 'Splodge' done. Splodge suits her, not so sure about the other name!!! How does Arthur feel about it. Now that's A name!! xx

I hope CP get more vouchers or more vets participating cos it's only the first week in March and the offer has weeks to run yet. Really good that people have asked for them though. And good for you Jules for getting 'Splodge' done. Splodge suits her, not so sure about the other name!!! How does Arthur feel about it. Now that's A name!! xx

schoedinger for a name makes me look smart...i need all the help i can get!!:thumbsup:

I suppose I should google this, but can't be bothered. lol.

I suppose I should google this, but can't be bothered. lol.

i posted a couple of wiki links....