Talks

A “derivation” of the Schrodinger wave equation based on simple calculus.
Learning Outcomes:
• 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.
• Dirac’s extension of these ideas to Einstein’s expression for the total energy of a particle: introduction to spin, antimatter, and the Standard Model of particle physics.

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.
Learning Outcomes:
• 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.
• When right- and left-travelling de Broglie waves (“corkscrews”) are added, as happens for a particle in a box, we get a complex standing wave whose magnitude is constant in time.

Learning Outcomes:
• 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.
• Understanding how these ideas apply to the atom, and how a LASER works (Light Amplification by Stimulated Emission of Radiation).

We will review the uncertainty principle of quantum mechanics, first formulated by Werner Heisenberg in 1927, and the role they played in the famous debate between Einstein and Bohr on the meaning of quantum theory. Along the way we will focus on questions like: what do we mean by "uncertainty", and how do we express that in the theory? What, in fact, is a physical property? Does a theory like quantum mechanics provide a description of physical reality? Interestingly, some of these questions do not have a unique answer.

Put two physicists in a room and ask them to talk about the interpretation of quantum mechanics. This is a recipe for disagreement; the mysteries of quantum theory run so deep that it’s hard to find any interpretive claims that are immune to controversy. Therefore, when thinking about quantum theory, it is a useful tactic to first focus on the macroscopic facts it predicts while ignoring the formalism and what it might suggest about the constitution of reality. I will adopt this tactic in my talk to describe the strange features of sequences of Stern-Gerlach measurements. This background will be enough to formulate the principle of “no information gain without disturbance” and the technological possibilities it implies, such as money that can’t be counterfeit and secure ways of distributing secret keys for cryptography. I’ll then move on to explain one idea about what might be going on at a deeper level – the idea of hidden variables. Finally, I’ll present Bell’s theorem, a result that reveals an uncomfortable tension between quantum mechanics and the theory of relativity.

The speculation that Dark Energy can be explained by the backreaction of present inhomogeneities on the evolution of the background cosmology has been increasingly debated in the recent literature. We demonstrate quantitively that the backreaction of linear perturbations on the Friedmann equations is small but is nevertheless non-vanishing. This indicates the need for an improved averaging procedure capable of averaging tensor quantities in a generally covariant way. We present an averaging process which decomposes the metric into Vielbeins selected employing a variational principle, and parallel-transports them to a single point at which they can be averaged. The functionality of the process is discussed in specific 2-d examples, and its application to 3-surfaces and metric recovery in cosmology is outlined.

One of the quintessential features of quantum information is its exclusivity, the inability of strong quantum correlations to be shared by many physical systems. Likewise, complementarity has a similar status in quantum mechanics as the sine qua non of quantum phenomena. We show that this is no coincidence, and that the central role of exclusivity in quantum information theory stems from the phenomenon of complementarity. We adopt an information-theoretic approach to complementarity, which leads to a new and simple definition of private states and new proofs of the achievable asymptotic rates of both secret key and entanglement distillation. From the latter follows a new proof of the direct part of the quantum noisy channel coding theorem.

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.
Learning Outcomes:
• 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.
• Why classical atoms cannot exist in our universe, and how the Heisenberg Uncertainty Principle and associated zero point energy stabilizes atoms, making their existence possible.