- #1
KastorPhys
- 3
- 0
By the Principle of Superposition, a state vector can be defined as pic.01
also, the state vector can represent a wave function in a continuous case as pic.02
My (1) question is, in pic.03, why the state vector can be pulled out from the integral?
I have an idea but I think it should be wrong:
------------
As shown in pic.02, the state vector is a set of values that each element is the value of the wave function, e.g. phi(0), phi(0.002), etc.
Thus, it can be considered as a constant since every elements will never change
Therefore, it can be pulled out from the integral
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However, this idea is fail to explain in the observable case.
Considering, in pic.04, question (2), Q is an operator which contain a momentum component, a differential operator. If the state vector is constant, it should give zero value when a momentum operator act on it and the Dirac representation will be failed.
So, if it is not a constant, how can it be pulled out from the integral?
========================
And my (2) question is that, in pic.04,
step 4 to step 5,
why the operator Q can skip the bra(x) vector and act on the state vector??
=========================
Thank you so much as I'm new in Quantum Mechanics!
also, the state vector can represent a wave function in a continuous case as pic.02
My (1) question is, in pic.03, why the state vector can be pulled out from the integral?
I have an idea but I think it should be wrong:
------------
As shown in pic.02, the state vector is a set of values that each element is the value of the wave function, e.g. phi(0), phi(0.002), etc.
Thus, it can be considered as a constant since every elements will never change
Therefore, it can be pulled out from the integral
-------------
However, this idea is fail to explain in the observable case.
Considering, in pic.04, question (2), Q is an operator which contain a momentum component, a differential operator. If the state vector is constant, it should give zero value when a momentum operator act on it and the Dirac representation will be failed.
So, if it is not a constant, how can it be pulled out from the integral?
========================
And my (2) question is that, in pic.04,
step 4 to step 5,
why the operator Q can skip the bra(x) vector and act on the state vector??
=========================
Thank you so much as I'm new in Quantum Mechanics!