Coursework focused on A Quantum Engineer’s Guide to Superconducting Qubits.
The Schrödinger equation is given as:
For the lowest energy level state , write the solution of . Then substitute it back in the Schrödinger equation and show it’s a solution. Use the time independent Schrödinger equation:
Which is equivalent to,
If then we know, ; because is a Hermite Polynomial
Plugged back into the time independent Schrödinger equation, we have:
The expectation value of a variable is given by . Show for the lowest energy state of the quantum harmonic oscillator that the expected value of the position is zero.
What is the Josephson oscillation frequency for a potential drop across a junction? Is this frequency change detectable by standard electronics? What voltage drop would give a Josephson oscillation frequency of ?
If , and
This frequency isn’t detectable by standard electronics