1it is
re^{-r/2}cos\theta =constant
is this in the book u told abt?
re^{-r/2}cos\theta =constant
where r is the radial distance of the point from origin
and theta is the colatitude (angle btw the radial vector and the one pointing towards the z coordinate of the point))
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5 Answers
49considering x-y slices throughout the volume!
i.e considering planes like z=a (a is a constant!) and trying out in each plane!
by symmetry, each plane will be divided into circles (contours) in which each point will have same r and magnitude of θ
so in each plane z=constant and is equal to r cos θ
re^{-r/2}cos\theta =constant
or, ze^{-r/2} =constant
so in each plane e^{-r/2} =constant
considering L to be the distance from the centre of each circle of constant r formed in each plane giving
L2+z2=r2
r=\sqrt{L^2+z^2}
again, we know for each circle, x2+y2=L2
giving, r=\sqrt{x^2+y^2+z^2}
so,
in each plane,
e^{\frac{\sqrt{x^2+y^2+k^2}}{2}}=const
where k is a const!
so we (class 12 students) can solve this by a great back stiffening process but higher people might be more conversant with solving the equation
ze^{\frac{\sqrt{x^2+y^2+z^2}}{2}}=const
usng the most coveted newton's laws of motion of quantum mechanics :P i.e. Schrodinger's equation!