QUANTUM TUNNELING AND SPIN

by Robert J. Nemiroff 

Michigan Tech

Physics X: About This Course

• Officially "Extraordinary Concepts in Physics"• Being taught for credit at Michigan Tech

o Light on math, heavy on concepts o Anyone anywhere is welcome

• No textbook requiredo Wikipedia, web links, and lectures onlyo Find all the lectures with Google at:

"Starship Asterisk" then "Physics X"  o http://bb.nightskylive.net/asterisk/viewforum.php?f=39

QUANTUM TUNNELING

The purely quantum mechanical ability for a particle to go through a barrier.

QUANTUM TUNNELING

A classical particle would fully reflect off the barrier.  

A quantum particle has chance to fully come out on the other side.  

The thicker the barrier, the smaller the chance.

Macroscopic objects have a diminishingly small chance of tunneling through a thick barrier.

QUANTUM TUNNELING

Examples of Quantum Tunneling:

• Radioactive decay o A particle tunnels out of a nucleus

• Scanning Tunneling Microscopeo measure tunneling electron current between a needle and

a surface.• Enzymes

o  a factor in reaction rates(!)

QUANTUM TUNNELING

What is the chance that a human can tunnel through a wall?

So small I could not find anyone willing to estimate this.  If you know of a specific numerical estimation, please tell me.

STERN- GERLACH EXPERIMENT

A beam of neutral particles with spin enters a non-uniform magnetic field.  Given that the particles can be divided into smaller particles that individually have electric charge, and that these particles are spinning, the non-uniform magnetic field would deflect a classical particle by an amount that depends on the orientation of the spin.  What actually happens?

1.  A continuum of deflections.2.  Only two discrete deflections show up, corresponding to "spin up" and "spin down" for neutral particles.

STERN- GERLACH EXPERIMENT

A classic experiment that shows a difference between quantum and classical mechanics.

STERN- GERLACH EXPERIMENT

2.  Only two discrete deflections show up, corresponding to "spin up" and "spin down" for neutral particles.

This is an amazing result.  No matter the initial orientations, the particles come out with only two possible spin values.  This is peculiar to quantum mechanics.

STERN- GERLACH EXPERIMENT

Now, one of the beams from the previous experiment is sent into a second Stern-Gerlach machine.  All of these particles have "spin up", but now the SG machine is on its side and can only deflect the particles left or right.  What happens?

1.  All of the particles are deflected to the left.2.  All of the particles are deflected to the right.3.  Half of the particles are deflected left, half right.4.  A continuum of left, right deflections is seen.

STERN- GERLACH EXPERIMENT

3.  Half of the particles are deflected left, half right.

This might not be surprising.  What might be surprising is that the orientation between the first and second SG devices need not be exactly 90 degrees to get a nearly 50 - 50 split.

But we are not done yet!

STERN- GERLACH EXPERIMENT

Now if one of THOSE beams is sent into a third SG experiment, along the original orientation, what happens?

1. One beam comes out.2. Two beams come out.3. A continuum of particles comes out.4. Nothing until someone plugs in the experiment.

STERN- GERLACH EXPERIMENT

 2.  Two beams come out.

This is really strange.  Shouldn't the particles all remember their orientation exiting the first Stern-Gerlach experiment?  They do not.  This is yet another non-classical result, fundamental to quantum mechanics.

STERN- GERLACH EXPERIMENT

The SG experiment demonstrates that the act of measuring something can affect its state.  If the second SG experiment had not been done, the third SG experiment would have found only a single beam of particles.  The act of measuring the spins of those particles in an orthogonal direction affected the quantum states of those particles, causing them to be measured differently the next time through.