Prove that if ?1(x) and ?2(x) are both solutions to the time-independent S.E. for a particular...
Prove that if ?1(x) and ?2(x) are both solutions to the
time-independent S.E. for a particular U0
(constant in x), then so is a?1(x) + b?2(x) with a and b constants.
Hint: Plug all 3 into the S.E.
then manipulate the equations for ?1(x) and ?2(x) to show you get
the equation for a?1(x) +b?2(x).
Homework Answers
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Prove that if ?1(x) and ?2(x) are both solutions to the
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Please prove this solution and explain why y2 can be taken as
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Prove that there are no natural number solutions to the equation where x, y ≥ 2...
Prove that there are no natural number solutions to the equation
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Prove that there are no natural number solutions to the equation where X, Y > 2. x2 - y2 = 1.
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(Variation of Parameters) (a) Find the two independent solutions x, (1) and x2 (t) of the homogeneous DE: x,-4x + 4x = 0 . (b) Find the Wronskian W(t) of your two solutions from Part (a). (c) Set up and solve the equations for the functions that we called c,() and c2(t), to use in finding a particular solution of the DE: x,,-4x + 4x = te2t Using Parts (a) and (c), set up the particular solution xp(t) Your answer...
Potential energy function,
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Assuming the time-independent Schrödinger equation, show that the following wave functions are solutions describing the one-dimensional harmonic behaviour of a particle of mass m, where ?2-h/v/mK, and where co and ci are constants. Calculate the energies of the particle when it is in wave-functions ?0(x) and V1 (z) What is the general expression for the allowed energies En, corresponding to wave- functions Un(x), of this one-dimensional quantum oscillator? 6 the states corresponding to the...
Please prove this solution and explain why y2 can be taken as
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Problem 2. Find the general solution of the equation Note that one of two linearly independent solutions is yi(r) -e. Solution. Using Abel's formula, we get the following relations for the Wronskian dW pi dW 2r1 On the other hand, Comparing these two expression for W(x), we can take y2 :- r2yı. Correspondingly, the general solution is
Problem 2. Find the general solution of the equation Note...
Note: The solutions for both parts of this problem are independent of the results of the previous problem. (a) For the descent of the rocket in the previous problem, do not neglect air resistance. Let the rocket feel a drag force proportional to the velocity 7-bmt. Find the velocity as a function of time and the terminal velocity. (b) Starting from the height in problem 1 and with bm 0.5, will the rocket reach terminal velocity before hitting the ground?...
1 Time-independent Schrödinger equation (TISE) Remember the (one-dimensional) time-independent Schrödinger equation (TISE) for a state ( definite energy E: with Now shift the potential energy by a constant: V(x) -> V(x) Vo Show that (a) The allowed energies (El,Ea. . .) are all shifted by Vo (b) The corresponding states (vi (x),P2( r),...) remain the same.
Prove that there are no natural number solutions to the equation
where x, y ≥ 2 ... (See Picture Below)
Prove that there are no natural number solutions to the equation where X, Y > 2. x2 - y2 = 1.
' )y" + 6xy = 0 about x。:0. #2.) (15 points) For ( 1-X Find two linearly independent solutions y,(x) and V2(x) (that is solve the recurrence relation.) This problem is difficult, so plan your time accordingly
' )y" + 6xy = 0 about x。:0. #2.) (15 points) For ( 1-X Find two linearly independent solutions y,(x) and V2(x) (that is solve the recurrence relation.) This problem is difficult, so plan your time accordingly
(2 points) is typed as lambda, a as alpha. The PDE a2u ar2 = yº ди ay is separable, so we look for solutions of the form u(x, t) = X(x)Y(y). When solving DE in X and Y use the constants a and b for X and c for Y. The PDE can be rewritten using this solution as (placing constants in the DE for Y) into X"/X (1/(k^2))(y^5)(Y'/Y) = -2 Note: Use the prime notation for derivatives, so the...
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