What is Quantum Tunneling, Exactly?

me being 14 and told to do the math equations im about pull a mathematical grind

My brain works the opposite direction. I have the hardest time with maths on their own, and learn them far better when I am applying them to systems that I have an understanding of.

Does this work with compression waves?

The particle outside the box needs to have sufficient energy to exist, correct?

Does quantum tunneling only work with charged particles?

A secret for u all. There are no electrons, around the atom there are magnetic wawes and it can go throu some objects

Did you restrict electron motion , and invented tunneling when it crosses barrier?

There is no such thing as quantum tunneling. Why? Because no physicist has ever measure the SAME electron twice. So no measurement inside or outside a box tells you anything about where an electron WAS.

For that side question "why can't a wave just abruptly end?" I think of this in terms of frequencies or momentum. If you take the Fourier transform of a wave that suddenly stops at a wall, the frequency spectrum is infinitely wide. Like for the particle in an infinite box, the wavefunction is continuous but not differentiable at the walls, which gives the momentum spectrum oscillations out to very high frequencies. With any real-world finite potential, the evanescent wave can make the momentum spectrum, or the spatial frequency spectrum, better contained and not oscillate out to infinity. Or another way to say it - you don't have enough energy to abruptly stop. The evanescent wave is a lower kinetic energy solution than a hard stop.

You are awesome . I am learning Quantum Physics in my Masters in Integrated Circuits and Systems here at IIT-Bombay in subject called Solid State Devices . While our professor did explain us for infinite potential well and the reason the electron cannot jump the barrier and be found on left or right 'top' sides of infinite potential well ( assuming infinite top is visible as is ) .

Our professor then goes on to explain the E<U problem ( finite potential well ) and now the solution of SWE , the wave function suggests the Electron to exist beyond the boundaries of finite potential well i.e. tunneling !!

I did hit me well , if this is the case then in infinite potential well as well we should be having some tunneling . Why is there no tunneling in that case ? And yes I realised my professor ( like you ) did nit specify the walls on sides of potential well are infinitely huge .

I like your introductions

Mathematics is the only way to look in four dimensions, literally.

Can anyone explain scanning tunneling microscopy?

Love the hadouken!

bugs bunny female version

AS YOU SAY RE PROOF REVIEW ALL MATH

DID ANYONE EVER SOLVE THAT FM TUNNEL EFFECT PROBLEM OR DID IT GO THE WAY OF HYPERIONISM FOR MOST?

no