Wavefunctions Live in Hilbert Space. What does it mean? What are Hilbert Spaces? In this video, I explore these ideas.
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𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬
A Hilbert space is a mathematical space where quantum states are represented as vectors. It is a type of inner product space, meaning we can define lengths (norms) and angles (inner products) between vectors, which helps describe concepts like superposition and probability in quantum mechanics.
This linear vector space is also complete, meaning it includes all possible states and their limits, ensuring the mathematics is consistent even for infinitely many quantum states. In this video I describe what Hilbert spaces are, in detail. I talk about Linear Vector spaces - Vector Addition, Scalar Multiplication. I also talk about Inner product, positive norm, completeness and separability.
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