If $\psi (x) = A (x^2 - a^2)$ is the wave function of an enclosed particle, find the normalization constant and the expected value of the energy. Compare the last result of the energy of the ground state how many times bigger is p smaller?
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The normalization condition is given by: ∫|Ψ(x)|^2 dx = 1 In this case, the wave function is Ψ(x) = A(x^2 - a^2). So, we need to calculate the integral: ∫|A(x^2 - a^2)|^2 dx = 1 Simplifying the expression inside the absolute value, we get: ∫|A(x^2 - a^2)|^2 Show more…
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