If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Physics library>Unit 17

Lesson 2: Atoms and electrons

# Quantum Wavefunction

In this video David gives an introductory explanation of what the quantum wavefunction is, how to use it, and where it comes from.

## Want to join the conversation?

• Why is there an imaginary unit in Schrodinger's equation? What does that mean?
• nice question.

As I see it, physically, it means that the wave function has no 'real' meaning until it is squared and then we get a real, physical quantity that can be measured.
• does this wave function also applies to photon?
• Nice question.

I am not a quantum expert but, as far as I know, ANY quantum system will have a wave function associated with it. Including photons, electrons, etc and, from what I understand, we are also part of a wave function when we are observing quantum phenomena. ie when we make an observation, the wave function collapses because we have (by observing it) made certain, something that was probabilistic.

So, until you observe the photon, it is defined by a wave function and its probabilty density is proportional to the square of the amplitude. When you have observed it , the wave function collapses.

mmm... hope that makes sense...
• This is bothering me.
What about the electrons through the double slit experiment? The scientists did observe a wave like pattern, no? How can the wave function then be considered as a probability function? Because if it were a probability function then we would have only observed it at specific places not like a wave, right?
Thanks very much!
• What actually happens when we perform the double slit experiment and record its outcome on a screen, is that we are making a measurement.

When an electron is observed it's wave function collapses except at that point, thus the electron exists only at said point and the observation is made. Before the measurement, the electron exists at multiple places at the same time (given by Schrodinger's eq.)
[refer Quantum superposition] {also refer Schrodinger's cat}

Each electron contributes to only one observation. However in the double slit experiment, we send a stream of electrons. In principle, more electrons end up where the probability is higher simply because the electrons are likely to end up there,and few electrons end up where the probability is less.

Hence, to put it simply, the wave pattern is formed due to individual electrons measured at different places , based on their actual numbers, which in-turn depend on the wave function.
• How did Schrödinger come up with this equation?
On coming up with it...how did he know that it was indeed consistent with laws of Thermodynamics?
• The Shrodinger Equation stems from the Hamiltonian, or the total energy equation, E = KE + PE and the equation for Psi = cos(kx-wt)+isin(kx-wt) = e^[i(kx-wt)] ─ doing a bit of multivariable calculus (since psi depends on both x and t) and some algebraic manipulation you'll find that everything begins to fit together, but there are a few other identities that you need to know; ie, k=2pi/wavelength and wavelength = h/p (as seen in the previous video) and that w = E/hbar where hbar=h/2pi.

Start with E = KE + PE = 1/2mv^2 + U (where U is the general potential energy) and rewrite the KE term as p*^2 / 2m , (p being momentum, since mv*mv*1/2*1/m =1/2mv^2.

Do the necessary partial derivatives on Psi (as seen in the Shrod. eq) and start substituting things around.

Mess around with that a bit and let me know if you get stuck, I'll be happy to go into further detail if you'd like, but this should give you a headstart :)
• Why not square the equation to begin with? Is there a use for it in it's 'unsquared'/normal state?
• I believe its because you must first solve the second order differential equation provided in the video to obtain the actual wave function.
• Schrodinger equation tells us what; the wave function of a single electron or of a system of an electron?
• This equation gives perfect results (in line with experimental data) when describing a single-electron system such as hydrogen or cations having only one electrons (for example He+)....
• At , what is X exactly?
• X denotes the position of a quantum particle in space. The wavefunction is a function of position (and time too, in Schrodinger's time dependent equation).
(1 vote)
• Why do we need to square the wave function when we already made it into absolute value already there?
|psi|
• the wave function is not wholly real. (it has an imaginary part to it)

So we can not measure it.

It only makes physical sense if it is squared.
• Consider a wave (Disturbance) in water.
As the wave propagates, the water molecules though stationary along the direction of propagation of wave move up and down.
So how does an electron behave like a wave? Does it have something like a water molecule moving up and down? I am unable to comprehend it.
• *If you think you understand quantum mechanics, you don't understand quantum mechanics* - RPF

On a serious note, the waves in both the situations are actually physicaly different, only the mathematical formulation is the same. In QM, the waves are probabilistic amplitudes, while the water waves are simple transverse/longitudinal periodic oscillations of the constituent particles. Probability waves simply mean they talk about the probability of finding the electron at a particular place. Why is it a wave like formulation, why is it so weird? Nobody knows. :)
• Is this electron wave is produced by electron? when the electrons produce this matter waves? Is there any connection with scattering of light?
• Electrons are excitations in the electron field. Photons are excitations in the electromagnetic field. Neither the electron or electromagnetic fields are the same as the quantum wave function.