In quantum mechanic the Hilbert space is often used. I don't study physics, must be said. So, I have a few questions to this space (I can calculate with complex numbers and vectors). 1. What's the different between a bra <p| and a ket |b> vector? 2. What calculation is behind that: <p|b>? 3. Is the Hilbert space a function room or a vector room? Because sometimes it is written |psi> (in Schrödinger equation => wave function) and sometimes it is written that the Hilbert space is a vector room. 4. How can a wave function be 1 (|psi|=1) or is the area under the function equal to 1 (integral)? 5. Is that definition: [A,B]=AB-BA (commutator)? 6. Can somebody solve me an example for this: int[ (psi*(x)) * (f(x)) ] dx 7. Why is the ... (dont know the name in English) value: A=<psi|A|psi>? Should be easy for you to answer this questions. Thanks.