Answered: By considering the integral ∫02π cosmlϕ…

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By considering the integral ∫₀^2π cosm_lϕ cosm'_lϕ dϕ, where m_l≠m'_l ,
confirm that the wavefunctions cosm_lϕ and cosm'_lϕ for a particle on a ring are orthogonal.

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By considering the integral ∫02π cosmlϕ cosm'lϕ dϕ, where ml≠m'l ,confirm that the wavefunctions cosmlϕ and cosm'lϕ for a particle on a ring are orthogonal.