can also be written as Show that the solutions of 1 d 1 X dr 2-X(x)...

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can also be written as Show that the solutions of 1 d 1 X dr 2-X(x) Y dy2Y(y) = -k if k is real and pikz X(x) = ) = {et ke Also show that these solutions are equivalent to X(x)= == -ikr sin ka cos kr X(x) = - Sekr 1 -kr * Y(y) = Y(y) Jsin ky cos ky if k is purely imaginary. Also show that X = sin k(ra), Y = sinh k(y - b) are solutions. = Y(y) = sinh k cosh ky = -ky can also be written as Show that the solutions of 1 d 1 X dr 2-X(x) Y dy2Y(y) = -k if k is real and pikz X(x) = ) = {et ke Also show that these solutions are equivalent to X(x)= == -ikr sin ka cos kr X(x) = - Sekr 1 -kr * Y(y) = Y(y) Jsin ky cos ky if k is purely imaginary. Also show that X = sin k(ra), Y = sinh k(y - b) are solutions. = Y(y) = sinh k cosh ky = -ky

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