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

• f 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 (classical) Indistinguishable (Quantum)

Bosons (integral spin s)

Fermions (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