Questions about some material from Dirac

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JasonJo
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Hey I was hoping you guys could clarify some stuff in Dirac, I'm trying to sort through the Schrödinger representation:

1) What exactly is the standard ket > ? Can anyone give me it in terms of pure linear algebra? What does it mean for it to be unity in terms of wave functions??

2) I guess Schrödinger's representation allows us to use only position and corresponding position derivatives to describe a physical system?

3) When we have the coefficient i in the equation for the quantum Poisson bracket, is this the complex i? Or is it an arbitrary coefficient.

4) When exactly can't we eliminate arbitrary phase factors? I know when the phase factor is a constant, we can take it such that it is unity when it is multiplied by it's conjugate.
 
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1) The standard ket is a vector in Hilbert space that describes the quantum state of a system. In terms of linear algebra, it is a vector in an inner product space, with the inner product being the probability amplitude of the system. It is unity if its norm (the absolute value of its inner product with itself) is equal to 1. This means that the amplitude of the wavefunction is equal to 1 for all points in space.2) Yes, Schrödinger's representation allows us to use only position and corresponding position derivatives to describe a physical system.3) Yes, the coefficient i in the equation for the quantum Poisson bracket is the complex i.4) We can't eliminate arbitrary phase factors when the phase factor is not a constant. In this case, we can only take it such that it is equal to 1 when it is multiplied by its conjugate up to a multiplicative constant.