Harmonic Oscillators Lecture 3 | Res. Assistant Çağdaş Ulus Ağca скачать в хорошем качестве

Harmonic Oscillators Lecture 3 | Res. Assistant Çağdaş Ulus Ağca

Demystifying building blocks of our universe using harmonic oscillators. This week, we will begin by tabulating the key results from the previous week and highlighting the differences between quantum mechanics and quantum field theory. Following that, we will apply the canonical quantization procedure to the Hamiltonian of a scalar field theory in a flat background. This Hamiltonian will resemble the harmonic oscillator Hamiltonian. We will then show that, by constraining the Hamiltonian to single-particle states in the non-relativistic limit, the Schrödinger equation emerges. Subsequently, we will examine the quantization of a scalar field in an expanding background, specifically in a Friedmann Universe. In this context, we will introduce the concept of conformal time and reformulate the scalar field action accordingly. Upon quantization, this system will reveal two distinct sets of observers. Based on their observations, we will see that there is no unique physical prescription for the vacuum state of a field in a general curved spacetime while illustrating that the harmonic oscillator framework remains consistent throughout.