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Let there be two operators,  = and V²(x, y, z) = + + ₂. Which of the following functions are eigenfunctions of  or V2? Which are the eigenvalues? a) y(x) = xª b) (x) = log(arx) c)(x) = exp(ax) d) (x) = cos(ax) e) y(x) = cos(ax) + isin(ax)

Let there be two operators,  = and V²(x, y, z) = + + ₂. Which of the following functions are eigenfunctions of  or V2? Which are the eigenvalues? a) y(x) = xª b) (x) = log(arx) c)(x) = exp(ax) d) (x) = cos(ax) e) y(x) = cos(ax) + isin(ax)

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Let there be two operators, Aˆ =∂/∂ x and ∇2(x, y, z) = ∂2/∂2x +∂2/∂2y +∂2/∂2z. Which of the followingfunctions are eigenfunctions of Aˆ or ∇2 ? Which are the eigenvalues?
a) ψ(x) = xa
b) ψ(x) = log(ax)
c) ψ(x) = exp(ax)
d) ψ(x) = cos(ax)
e) ψ(x) = cos(ax) + isin(ax)

Let there be two operators,  = and V²(x, y, z) = ₁+ ²+₂. Which of the following functions are eigenfunctions of  or V2? Which are the eigenvalues? a) (x) = xa b) (x) = log(ax) c)(x) = exp(ax) d) (x) = cos(ax) e) (x) = cos(ax) + isin(ax)
Transcribed Image Text:Let there be two operators,  = and V²(x, y, z) = ₁+ ²+₂. Which of the following functions are eigenfunctions of  or V2? Which are the eigenvalues? a) (x) = xa b) (x) = log(ax) c)(x) = exp(ax) d) (x) = cos(ax) e) (x) = cos(ax) + isin(ax)
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