Consider an infinite potential well with the width a. What happens to the ground state wavelength if the width decreases? O It does not change. O It will increase. O It will decrease.
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- Consider an infinite square well with wall boundaries x=0 and x=L. Explain why the function (x)=Acoskx is not a solution to the stationary Schrödinger equation for the particle in a box.Check Your Understanding Suppose that a particle with energy E is moving along the x-axis and is in the region O and L. One possible wave function is (x,t)={AeiEt/hsinxL, when 0xL otherwise Determine the normalization constant.A particle of mass m confined to a box of width L is in its first excited state 2(x). (a) Find its average position (which is the expectation value of the position). (b) Where is the particle most likely to found?
- Check your Understanding (a) Consider an infinite square well with wall boundaries x=0 and x=L. What is the of finding a quantum panicle in its state somewhere between x=0 and x=L/4? (b) Repeat question (a) for a classical panicle.What is the ground state energy (in eV) of an a -particle confined to a one-dimensional box the size of the uranium nucleus that has a radius of approximately 15.0 fm?Find the expectation value of the kinetic energy for the particle in the state, (x,t)=Aei(kxt). What conclusion can you draw from your solution?
- A particle is confined to the one-dimensional infinite potential well of If the particle is in its ground state, what is its probability of detection between (a) x = 0 and x = 0.25L, (b) x = 0.75L and x = L, and (c) x = 0.25L and x = 0.75L?A proton is confined to a one dimensional infinite potential well 100 pmwide. What is its ground-state energy?A proton is confined to a one-dimensional infinite potential well 100 pm wide.What is its ground-state energy?
- The ground-state energy of an electron trapped in a onedimensional infinite potential well is 2.6 eV.What will this quantity be if the width of the potential well is doubled?What is the ground-state energy of (a) an electron and (b) a proton if each is trapped in a one-dimensional infinite potential well that is 200 pm wide?A particle is in the ground state of a box of length L (i.e. an infinite potential well). Suddenly the box ex- pands (symmetrically) to twice its size, leaving the wave function undisturbed. What is the probability of finding the particle in the ground state of the new box?