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Simfish
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To me, braket notation just seems much easier and more intuitive than the approach from Griffiths. And yes, I learned QM through a text that used braket notation.
Simfish said:To me, braket notation just seems much easier and more intuitive than the approach from Griffiths. And yes, I learned QM through a text that used braket notation.
Simfish said:To me, braket notation just seems much easier and more intuitive than the approach from Griffiths. And yes, I learned QM through a text that used braket notation.
Roger Penrose said:I recall that when I was about to enter university to study mathematics I had expected to find that the others, who would be my mathematical colleagues, would think more-or-less as I did. It had been my experience at school that my classmates seemed to think rather differently than myself, which I had found somewhat disconcerting. 'Now', I had though to myself excitedly, 'I shall find colleagues with whom I can much readily communicate! Some will think more effectively than I, and some less; but all will share my particular wavelength of thought.' How wrong I was! I believe that I encountered more differences in modes of thinking that I had ever experienced before!
I'm not going to read all that, but the appearence of all those integrals in the messy calculation suggests to me that the difference between it and the "bra-ket" calculation is that the messy one uses the explicit definition of the inner product on L2(ℝ3) (over and over, without ever using the result that it is an inner product), while the "bra-ket" calculation pays no attention to which inner product we're dealing with. You don't need bra-ket notation to do that.Simfish said:It seems that braket notation makes some problems A LOT cleaner, which in turn, makes them easier for me to understand. Here's an example (with a simple harmonic oscillator): http://www.scribd.com/doc/45874729/SHO-3. The matrix method and "doing the integrals in x-space" method are FAR messier than the braket notation method.
Simfish said:To me, braket notation just seems much easier and more intuitive than the approach from Griffiths. And yes, I learned QM through a text that used braket notation.
Simfish said:To me, braket notation just seems much easier and more intuitive than the approach from Griffiths. And yes, I learned QM through a text that used braket notation.
Braket notation, also known as Dirac notation, is a mathematical notation used in quantum mechanics to represent quantum states, operators, and measurements. It simplifies complex mathematical equations and helps to visualize and understand the concepts of quantum mechanics more easily.
Braket notation uses a combination of angle brackets and vertical bars to represent quantum states and operators, while traditional mathematical notation uses symbols and equations. Braket notation also allows for more intuitive manipulation and calculation of quantum states and operators.
While it is not absolutely necessary to learn braket notation to understand quantum mechanics, it is widely used in the field and can greatly enhance one's understanding of the concepts. It is also used in many textbooks and research papers, so learning it can be beneficial for further studies in the field.
One potential drawback of braket notation is that it may be initially confusing for those who are more familiar with traditional mathematical notation. It also requires some mathematical background and understanding of linear algebra concepts. However, with practice, it can become a powerful tool for understanding and working with quantum mechanics.
While braket notation was originally developed for quantum mechanics, it has since been adapted and used in other fields such as quantum computing, quantum information theory, and quantum optics. It can also be applied to other areas of physics where linear algebra is used, such as in electromagnetism and mechanics.