Visualization of electron as a wave

[spiffing_abhijit]

well i have understood that bohr's model had a flaw and i have understood that electrons can orbit those radii around the nucleus where nk=2*3.14r where they behave like standing waves.i am not able to visualize the nature of electron as a wave particularly standing,eg we can visualize matter waves but how can we visualize this that too around nucleus and the concept of orbitals has blown my mind.what is the need of these orbitals first.then spin confuses me a lot.why had spin been introduced and whatis its physical significance.i was comfortable with bohr's model but the truth that electrons don't move around the nucleus like we saw earlier has cofused me a lot especially it's visualization as a wave.pls clear my concepts regarding orbitals and how electrons move around these orbitals as waves.it will be a great humanitarian help. i promise.

 

[malawi_glenn]

You can't visualize how the electron moves in the atom, you must work out the wave functions which tells you with what probability the electron is located at a certain radius, polar angle and azimutal angle. This you can do by solving the spherical schrödinger equation: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydwf.html
http://www.falstad.com/qmatom/

free electrons propagate as a "wave" in that sense that it has a deBroigle wavelength: (plane wave solution to SE, also called deBroigle wavefunction)
$$\Psi (\vec{x},t) = N e^{i(\vec{p}\cdot\vec{x}-Et)}$$

Remember that the 'wave nature' of particles has to do with its wave function, it is not like a water wave or a standing wave on a string.

So the concept in QM is that we can't really say how things move etc, we can only work out the wave function and what observables that it contains. I hope you are familiar with Heisenbergs uncertainty relation: $$\Delta x \Delta p > \hbar$$, so if you know where the particle are, then you have no idea of what its momentum is.

Spin is an intrinsic degree of freedom for subatomic particles. Angular momentum we can derive from rotation symmetry in 3D, and we will obtain commutator relations for angular momentum operators. Then we see what happens if we move to 2D, and then we get spin.

Spin is manifested in how particles react on magnetic and electric fields. Compare with classical magnetic dipoles.
-> Stern-Gerlach experiment

 

[spiffing_abhijit]

Thanks