We are looking for the solution of the harmonic oscillator problem (Vˆ =1/2kx2). To do so: • we are going the use the following normalized trial function: –square root of15/16a5 (a2 − x2). – a is the variation parameter. – The particle is confined between [-a,a]. Which is the better approximation for the energy we can obtain applying the simple variation method? It might be useful to know the following relations: • a−a(a2 − x2)dx =4a3/3; a−a x2(a2− x2)dx =16a7/105
We are looking for the solution of the harmonic oscillator problem (Vˆ =1/2kx2). To do so: • we are going the use the following normalized trial function: –square root of15/16a5 (a2 − x2). – a is the variation parameter. – The particle is confined between [-a,a]. Which is the better approximation for the energy we can obtain applying the simple variation method? It might be useful to know the following relations: • a−a(a2 − x2)dx =4a3/3; a−a x2(a2− x2)dx =16a7/105
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We are looking for the solution of the harmonic oscillator problem (Vˆ =1/2kx2). To do so:
• we are going the use the following normalized trial function:
–square root of15/16a5 (a2 − x2).
– a is the variation parameter.
– The particle is confined between [-a,a].
Which is the better approximation for the energy we can obtain applying the simple
variation method?
It might be useful to know the following relations:
• a−a(a2 − x2)dx =4a3/3; a−a x2(a2− x2)dx =16a7/105
![We are looking for the solution of the harmonic oscillator problem (V = kx²). To do so:
• we are going the use the following normalized trial function:
√1655 (a²-x²).
-a is the variation parameter.
The particle is confined between [-a,a].
Which is the better approximation for the energy we can obtain applying the simple
variation method?
It might be useful to know the following relations:
f(a²-x²)dx = 4g³; fax²(a²-x²)²dx = 16a7
105
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Transcribed Image Text:We are looking for the solution of the harmonic oscillator problem (V = kx²). To do so:
• we are going the use the following normalized trial function:
√1655 (a²-x²).
-a is the variation parameter.
The particle is confined between [-a,a].
Which is the better approximation for the energy we can obtain applying the simple
variation method?
It might be useful to know the following relations:
f(a²-x²)dx = 4g³; fax²(a²-x²)²dx = 16a7
105
●
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