7. Schrödinger's equation A particle of mass m moves under the influence of a potential given by the equation -{" 0 U(x)= si x a where a is half the width of the potential well. Consider that the energy of the particle. E, is such that -W

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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
Transcribed Image Text: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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