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  1. bananabandana

    I Negative and Positive energy modes of KG equation

    If we have the normal KG scalar field expansion: $$ \hat{\phi}(x^{\mu}) = \int \frac{d^{3}p}{(2\pi)^{3}\omega(\mathbf{p})} \big( \hat{a}(p)e^{-ip_{\mu}x^{\mu}}+\hat{a}^{\dagger}(p)e^{ip_{\mu}x^{\mu}} \big) $$ With ## \omega(\mathbf{p}) = \sqrt{|\mathbf{p}^{2}|+m^{2}}## Then why do we associate...
  2. bananabandana

    I Degenerate Perturbation Theory

    I'm struggling to understand degenerate perturbation theory. It's clear that in this case the 'normal' approximation method fails completely seeing as you get a divide by zero. I follow the example for a two state system given in e.g D.J Griffiths "Introduction to Quantum Mechanics" However...
  3. bananabandana

    Definition of an Ensemble

    Homework Statement Confused about what a statistical ensemble actually means. Why does the ensemble have to have a uniform probability distribution at equilibrium? [If my definition of an ensemble is correct] 3. The Attempt at a Solution This is what I understand so far: For any given...