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InterviewSolution
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(b) What are normalized and orthogonal wave functions |
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Answer» Anormalized wavefuntion means that the probability that the particle is found in the considered domain is equal to 1 and thus the integral of the square of thewave functionin the domain is equal to 1 (remind that thewave functionis afunctionof complex variable) as previously written by Matùs Dubecký.… “Orthogonal” means “perpendicular.” For perpendicular vectors, their dot product is zero. (Cosine of 90 degrees is zero.) You can compute the dot product by multiplying together the corresponding vector elements (that is, 1 with 1, 2 with 2, 3 with 3, …) and then adding together all of these products.Functions can be orthogonal too, because functions can be like vectors with an infinite number of elements. However, in this extension, you can no longer sum the products of elements—you must integrate the product of the two functions. (For complex valued functions, it’s a bit more complicated.) |
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