1. The equation means that the eigenvalue of on is 0:

2. The length of the vector is 0:

3. The physical meaning is that the probability of the system being at state is 0.

In other words, there is no state with an eigen-energy lower than the ground state one.

4. For the equation , the 0 at the right is a scalar.

5. For the equation , the 0 at the right is a zero vector – a state vector with length zero.

6. is a state vector. However, it is NOT the zero vector.

Instead, it is the state vector of the ground state. Its length is 1 unit.

— Me@2015-11-03 03:26:58 PM

2015.11.04 Wednesday (c) All rights reserved by ACHK