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pivoxa15
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Does it surprise you that the fundalmentals of wave mechanics fits so nicely into an inner product space. I assume this kind of algebra existed long ago but QM seem to fit perfectly into it. How amazing is that?
Maybe it's because waves are written with exponentials, and and so a product of two waves is still an exponential, and the derivative too?pivoxa15 said:Does it surprise you that the fundalmentals of wave mechanics fits so nicely into an inner product space. I assume this kind of algebra existed long ago but QM seem to fit perfectly into it. How amazing is that?
pivoxa15 said:Does it surprise you that the fundalmentals of wave mechanics fits so nicely into an inner product space. I assume this kind of algebra existed long ago but QM seem to fit perfectly into it. How amazing is that?
Wave mechanics, also known as quantum mechanics, is a branch of physics that explains the behavior of particles at a microscopic level. It is based on the concept of waves, which describe the probability of finding a particle in a certain location.
Inner product spaces are mathematical structures that allow for the measurement of distance and angles in a vector space. In wave mechanics, inner product spaces are used to calculate the probability of finding a particle in a certain state or location.
Wave mechanics is used in a variety of fields, including chemistry, material science, and engineering. It is also the basis for modern technologies such as transistors, lasers, and magnetic resonance imaging (MRI).
One of the main challenges in studying wave mechanics is the abstract nature of the concepts involved. It can be difficult to visualize and understand the behavior of particles at a microscopic level. Another challenge is the complex mathematical calculations required to solve problems in wave mechanics.
Classical mechanics, also known as Newtonian mechanics, is based on the laws of motion and is used to describe the behavior of macroscopic objects. Wave mechanics, on the other hand, is used to describe the behavior of particles at a microscopic level and is based on the concept of waves rather than particles.