Show how the wave function of the even states of a particle in an infinite well...

Show how the wave function of the even states of a particle in an infinite well extending from x=-L/2 to x=L/2 evolve in time. Details!

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genius_generous answered 2 years ago

1.Normalize the wave function for a particle in infinite potential well? 2.What is the Tunnel effect?...

1.Normalize the wave function for a particle in infinite potential well? 2.What is the Tunnel effect? Calculate depth of penetration in a potential barrier-Which attenuation is to be used as standard for this calculation?

Consider a particle of mass ? in an infinite square well of width ?. Its wave...

Consider a particle of mass ? in an infinite square well of width ?. Its wave function at time t = 0 is a superposition of the third and fourth energy eigenstates as follows: ? (?, 0) = ? 3i?3(?)+ ?4(?) (Find A by normalizing ?(?, 0).) (Find ?(?, ?).) Find energy expectation value, <E> at time ? = 0. You should not need to evaluate any integrals. Is <E> time dependent? Use qualitative reasoning to justify. If you measure...

For a particle in an infinite potential well the separation between energy states increases as n...

For a particle in an infinite potential well the separation between energy states increases as n increases (see Eq. 38-13). But doesn’t the correspondence principle require closer spacing between states as n increases so as to approach a classical (nonquantized) situation? Explain.

How the wave function and wave packets can be used to explain the particle-wave properties of...

How the wave function and wave packets can be used to explain the particle-wave properties of electrons?

Show that the bound state wave function of the δ function's well is well orthogonal to...

Show that the bound state wave function of the δ function's well is well orthogonal to all scattering state wave functions.

Consider a particle in an infinite square well, but instead of having the well from 0...

Consider a particle in an infinite square well, but instead of having the well from 0 to L as we have done in the past, it is now centered at 0 and the walls are at x = −L/2 and x = L/2. (a) Draw the first four energy eigenstates of this well. (b) Write the eigenfunctions for each of these eigenstates. (c) What are the energy eigenvalues for this system? (d) Can you find a general expression for the...

A particle in an infinite one-dimensional square well is in the ground state with an energy...

A particle in an infinite one-dimensional square well is in the ground state with an energy of 2.23 eV. a) If the particle is an electron, what is the size of the box? b) How much energy must be added to the particle to reach the 3rd excited state (n = 4)? c) If the particle is a proton, what is the size of the box? d) For a proton, how does your answer b) change?

An infinite potential well in one dimension for 0 ≤ x ≤ a contains a particle...

An infinite potential well in one dimension for 0 ≤ x ≤ a contains a particle with the wave function ψ = Cx(a − x), where C is the normalization constant. What is the probability wn for the particle to be in the nth eigenstate of the innite potential well? Find approximate numerical values for w1, w2 and w3.

A particle in the infinite square well (width a) starts out being equally likely to be...

A particle in the infinite square well (width a) starts out being equally likely to be found in the first and last third of the well and zero in the middle third. What is the initial (t=0) wave function? Find A and graph the initial wave function. What is the expectation value of x? Show your calculation for the expectation value of x, but then say why you could have just written down the answer. Will you ever find the...

Find the energy spectrum of a particle in the infinite square well, with potential U(x) →...

Find the energy spectrum of a particle in the infinite square well, with potential U(x) → ∞ for |x| > L and U(x) = αδ(x) for |x| < L. Demonstrate that in the limit α ≫ hbar^2/mL, the low energy part of the spectrum consists of a set of closely-positioned pairs of energy levels for α > 0. What is the structure of energy spectrum for α < 0?

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