Some intuiontal questions concerning Sakurai's QM.

[Kontilera]

Some intuitional questions concerning Sakurai's QM.

Hello!
I've just started reading Sakurai 's 'Mordern Quantum Mechanics' and open this thread for smaller intuitonal wonderings / questions. Some of them I might be able to solve myself with some help from you guys and others are of the sort that I'll just need clarification from people with a better understanding of QM and the mathematics.

If you think I'm close to the answer feel free to not answer the whole question but just give some leading points. :)
So far my wonderings are:

1. The relation between ket's and bra's is a complex conjugation of the vector/function. Is there any mathematical term for spaces with this kinds of metrics (it doesn't seem like a metric describing a Riemannian manifold)? Is there any pro's or cons to consider the hilbert space as a tangent space of a bigger structure, a manifold? I.e. will I encounter concepts such as parallell transport in QM later?


2. Sakuari talks about how the measurements 'destroys information' of the previous state. Where can I find more information about this? It seems as if I should have heard about it before since the lost of information is a big deal in physics. :)

Thanks really much!


ps. tried to correct the title but the edit doesn't seem to update it.

 

[eljose79]

Hello! It's great that you're diving into Sakurai's 'Modern Quantum Mechanics' and exploring the intuitive aspects of the subject. I'll try my best to answer your questions and provide some insights.

1. The relation between kets and bras is indeed a complex conjugation, and the mathematical term for spaces with this kind of metric is a Hermitian metric. This metric is used in quantum mechanics to define the inner product between kets and bras, which is essential for calculating probabilities and performing measurements. As for considering the Hilbert space as a tangent space of a bigger structure, it is possible to do so and it has been explored in certain approaches to quantum gravity. However, in standard quantum mechanics, the Hilbert space is considered as a complete space in itself and we do not encounter concepts like parallel transport.

2. The concept of measurement in quantum mechanics is a complex and debated topic. The idea of "destroying information" is related to the collapse of the wavefunction after a measurement is performed. This collapse results in a loss of information about the previous state of the system, as only the outcome of the measurement is known. This is also known as the measurement problem in quantum mechanics, and there are different interpretations of how to understand it. Some suggest that the measurement process is inherently random and unpredictable, while others propose that there are hidden variables at play. I recommend looking into the Copenhagen interpretation, the many-worlds interpretation, and the de Broglie-Bohm theory for more information on this topic.

I hope this helps to clarify some of your questions. Keep exploring and asking questions, and best of luck with your studies!