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7. Schrödinger's equation A particle of mass m moves under the
influence of a potential given by the equation
U(x)
-W
0
where a is half the width of the potential well.
Consider that the energy of the particle. E, is such that -W<E<o. Show that if
we only consider states of the particle with even functions, then it holds that:
tan (ja)
¹ (ja) = ²/1,
where
j²
22
si x < a
si x > a
=
=
2m(E + W)
h²
2mE
h²

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