Explain normalised and orthogonal wave function?
Question: Explain normalised and orthogonal wave function?
I will explain what normalised and orthogonal wave functions are, and why they are important in quantum mechanics. Normalised wave functions are wave functions that have a total probability of one, meaning that the integral of their squared modulus over all space is equal to one. This ensures that the wave function is physically meaningful, as it represents the probability density of finding a particle in a given region of space. Orthogonal wave functions are wave functions that have a zero inner product with each other, meaning that the integral of their product over all space is equal to zero. This implies that they are linearly independent, and can form a basis for the Hilbert space of possible wave functions. Orthogonal wave functions are useful for solving the Schrödinger equation, as they allow us to express any wave function as a linear combination of them, and find the corresponding energy eigenvalues and eigenstates.
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