Recent content by hello_world30

  1. hello_world30

    I Proving that ##\omega_0^2 < 2g/l ## for a simple pendulum.

    is there a way to solve it using lagrange multipliers ?
  2. hello_world30

    I Proving that ##\omega_0^2 < 2g/l ## for a simple pendulum.

    Here is the problem : A pendulum is composed of a mass m attached to a string of length l, which is suspended from a fixed point. When hanging at equilibrium, the pendulum is hit with a horizontal impulse that results in an initial angular velocity ω0. Show that if ω20 < 2g/l, the string will...
  3. hello_world30

    A Hamiltonian in second quantization

    Thank you for your prompt reply. Why is it that if I substitute x and p operators that are exressed in terms of a and a^(+) into the Hamiltonian , it does not have the 1/2 hbar omega term, but when I use the conventional way of deriving the Hamiltonian (starting from aa^+) then I get a...
  4. hello_world30

    A Hamiltonian in second quantization

    Hello ! I require some guidance on this prove :I normally derive the Hamiltonian for a SHO in Hilbert space with a term of 1/2 hbar omega included. However, I am unsure of how one derives this from Hilbert space to Fock space. I have attached my attempt at it as an image below. Any input will be...
    • hello_world30
    • Thread
    • Hamiltonian Quantization Quantum and general physics Second quantization
    • Replies: 4
    • Forum: Quantum Physics