EP 228: Quantum Mechanics lecture 19 Identical particles , quantum - PowerPoint PPT Presentation

EP 228: Quantum Mechanics lecture 19 Identical particles , quantum computer

Multi-particle system • Helium atom will have two electrons - • If we ignore the interactions between the two electrons, then the potential energy of the helium atom will be sum of potential energy of each electron with two protons inside the nucleus Even if the interactions are included, there is a principle called Pauli ’ s exclusion principle which is obeyed by system of electrons. The principle states ``no two electrons can share the same set of quantum numbers ’’

Can we see this from Schrodinger equation for non-interacting system of two electrons?

System of identical particles System of identical particles Distinguishable Indistinguishable (classical) (Quantum) Bosons Fermions (integral spin s) (half-odd integral s)

System of two identical particles

Prob. Density Not same

Quantum Computers • Qubits – two states of spin ½ electrons • Powerful than classical bits because we can have superposition of qubits • Algorithms involving qubits (quantum algorithms) have been shown to be efficient compared to classical algorithms