Here is your opportunity to experience, online, select content from Perimeter Institute's highly successful two-week International Summer School for Young Physicists (ISSYP). While we could reach up to 100 "young physicists" per year with our onsite ISSYP camps, our Virtual ISSYP opens up this fantastic learning experience for all to enjoy. The Virtual ISSYP is intended for students, teachers and anyone interested in learning more about the wonders of modern physics and the excitement of research and discovery at the frontiers of knowledge.
A “derivation” of the Schrodinger wave equation based on simple calculus.
• How to express the de Broglie wave of a free particle, i.e. a complex traveling wave, in terms of the particle’s energy and momentum, and how to differentiate this wave with respect to its space and time variables (x and t).
• How to combine the above mathematical results with the Newtonian expression for the total energy of a particle to get Schrodinger’s wave equation.
The de Broglie waves we have been using thus far were assumed to be real functions; we discuss why this is wrong and how to fix the problem.
• Understanding why there is a serious flaw with using real de Broglie waves, and how using a complex wave (one with both a real and an imaginary part) solves the problem.
• Understanding how the de Broglie wave corresponding to a free particle is like a moving corkscrew, with a magnitude that is uniform across space and constant in time.
• How the complex standing wave states of an electron in a one-dimensional box are “stationary states” in that the electron probability pattern is static (not changing with time).
• However, if the electron is put in a superposition of two such stationary states (with different energies), its probability pattern is not static, but rather oscillates back and forth; understanding how this oscillation is connected with photon emission and absorption.
A discussion of how the zero point energy of atoms is what makes possible their existence in our universe – atoms are purely quantum mechanical objects.
• Continuation of QM-9: A calculus-based derivation of the zero point energy of the quantum harmonic oscillator.
• How our previous understanding of energy quantization and zero point energy can be applied also to the hydrogen atom.
Understanding the zero point energy of the quantum harmonic oscillator as a consequence of the Heisenberg Uncertainty Principle.
• Understanding why the minimum energy of a ball in a bowl must be greater than zero based on the Heisenberg Uncertainty Principle.
• How the Heisenberg Uncertainty Principle adds a purely quantum mechanical kinetic energy to the ball, in addition to its classical potential energy.
A discussion of the space and time axes of a moving observer and an introduction to length contraction.
• Understanding why and by how much a moving observer’s position axis is “tilted in time.”
• Understanding how a moving platform appears to a stationary observer.
• Beginning to understand the cause of length contraction.
A continuation of the SR-10 discussion on length contraction. Resolving Principle 2*.
• Relativity of simultaneity revisited – gaining a deeper understanding of what it means.
• A full understanding of the nature of length contraction based on relativity of simultaneity.
• Resolving a key paradox in special relativity: Principle 2*, introduced in SR-4. How it is possible to measure the same speed for the light whether you are running toward or away from a flashlight.
Taking our intuitive understanding of the quantum world gained by studying a particle in a one-dimensional box, we generalize to understand a quantum harmonic oscillator.
• Introduction to the classical physics of a ball rolling back and forth in a bowl, a simple example of a very important type of bounded motion called a “harmonic oscillator.”
• The quantization of allowed energies of a harmonic oscillator: even spacing between energy levels, and zero point energy.
By applying our understanding of the quantum harmonic oscillator to the electromagnetic field we learn what a photon is, and are introduced to “quantum field theory” and the amazing “Casimir effect.”
• Understanding that classical electromagnetic waves bouncing around inside a mirrored box will exist as standing waves with only certain allowed frequencies.
Space obeys the rules of Euclidean geometry. Spacetime obeys the rules of a new kind of geometry called Minkowskian geometry.
• Triangles in spacetime obey a Pythagoras-like theorem, but with an unusual minus sign.
• The true nature of time as geometrical distance in spacetime.
• How to analyse and resolve the Twins’ Paradox using spacetime diagrams in combination with Minkowskian geometry.