## Quantum Mechanics for BC Calculus Students

You’ve painstakingly acquired the knowledge to take the AP Calculus BC exam, and now you’re wondering what to do next – why not learn quantum mechanics? This is a serious challenge for dedicated students, but well worth the effort!

Locations: San Jose

Cost: \$120

Recommended hours: 8-12

Goals:

• Learn quantum mechanics concepts such as energy quantization, atomic orbitals, and electron tunneling
• Apply the knowledge from every chapter of Calculus BC to develop understanding of quantum mechanics

## Course Description:

No prior knowledge of quantum mechanics is necessary, though some familiarity with chemistry is recommended.  This course covers three main topics, each with three parts which explore wavefunctions and the Schrodinger equation.  Students will solve differential equations, find quantized energy levels, approximate solutions with power series, and generally be amazed at the power of calculus.

Starting with a short introduction to wavefunctions and solving differential equations, we then dive into the three topics: the harmonic oscillator, atomic orbitals (specifically s-orbitals), and electron tunneling, which is necessary for electron microscopes (among other things).

Students must have completed Calculus BC or equivalent and be ready for rigorous attention to detail to get the most out of this 1-on-1 course.

## Course Topics

The harmonic oscillator

Approached from two different perspectives (starting with the wavefunction and starting with energy quantization). Students will see how energy quantization comes naturally from trig functions and practice approximating solutions using power series.

Atomic orbitals

Specifically the s-orbitals.  Students will calculate the 1s and 2s orbital wavefunctions for the hydrogen atom directly from the Schrodinger equation, which will allow them to calculate properties of the orbitals such as average distance from the nucleus.

Electron tunneling.

Electron tunneling is necessary for electron microscopes among other things.  Students will start with exploring the famous particle-in-a-box scenario and the ‘quantum corral,’ then perform a difficult calculation to find the wavefunction for an electron that is tunneling through a wall (what is the probability it will pass through the “impenetrable” wall?).

## Make the Most of the Summer!

Students who stay actively engaged in the learning process during the summer perform better during the school year.