# Is it vacum state is orthogonal or not?

1. Feb 2, 2010

### razif

1. The problem statement, all variables and given/known data
$$\left\langle0_{x}|0_{y}\right\rangle$$ is this orthogonal or not?

2. Relevant equations
for $$\left\langle1_{x}|1_{y}\right\rangle$$ we already know that this state is orthogonal to each others because 1 state at x-axis while the others in y-axis

for $$\left\langle1_{x}|1_{x}\right\rangle$$ we know that this state is not orthogonal to each others because they were in same axis

for $$\left\langle0_{x}|0_{x}\right\rangle$$ we can say that this state not orthogonal to each other because both vacum state in same x-axis

3. The attempt at a solution

but for $$\left\langle0_{x}|0_{y}\right\rangle$$ can we say that this state is not orthogonal to each others?because both of them are vacum state although it written that the vacum state at x-axis and vacum state at y-axis, if yes this is not orthogonal, can someone point me the reason. I just assumed that because both state are in vacum state and they can be at any axis without changing any state at that axis.