Solve Particle in a Box Questions: Lowest Energy & Probability

[Physicsiscool]

Can someone please explain to me how I should go about solving the following 2 questions?

#1 The lowest energy level in a particle confined to a one-dimensional region of space with fixed dimension "L" is Eo. If an identical particle is confined to a similar region with the fixed distance (1/4)L, what is the energy of the lowest energy level that the particles have in common? Express in terms of Eo.

#2 Consider a particle in a box of width "L" and let the particle be in a state n = 11. What is the first value of x, larger then 0, where the probability of finding the particle is the highest?

 

[dextercioby]

Can someone please explain to me how I should go about solving the following 2 questions?

#1 The lowest energy level in a particle confined to a one-dimensional region of space with fixed dimension "L" is Eo. If an identical particle is confined to a similar region with the fixed distance (1/4)L, what is the energy of the lowest energy level that the particles have in common? Express in terms of Eo.

#2 Consider a particle in a box of width "L" and let the particle be in a state n = 11. What is the first value of x, larger then 0, where the probability of finding the particle is the highest?

I have the awkward feeling I've seen these 2 problems somewhere on this forum;perhaps one of the moderators/science advisors/homework helpers could give u the link.I couldn't since i don't have a statute/etiquette on this forum.
But I'm interested in one...Guys,can u tell me what i need to do to get me label of science advisor/homework helper ?

 

[da_willem]

Can someone please explain to me how I should go about solving the following 2 questions?

You should solve the Schrödinger equation with the 'infinite square well potential': V=0 between 0<x<L or -(1/2)L<x<(1/2)L or something like that and V=infinite outside this region. The given that the particle is confined to this region gives you your boundary condition.

 

[silverpig]

For #1 the energy levels of the box go as 1/L^2

So substitute in L/4 for L and you'll have the energy (16 Eo if I do my math right)

 

[da_willem]

That sounds right. Now for the second question you need the wave function, if this is not given you will still have to solve the Schrödinger equation or have an idea of what the solution will look like...