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2. A particle of mass m in the infinite square well of width a (located at...
2. A particle of mass m in the infinite square well of width a at time...
2. A particle of mass m in the infinite square well of width a at time 1 - 0 has wave function that is an equal weight mixture of the two lowest n= 1,2 energy stationary states: (x,0) - C[4,(x)+42(x)] (a) Normalize the wave function. Hints: 1. Exploit the orthonormality of W, 2. Recall that if a wave function is normalized at t = 0, it stays normalized. (b) Find '(x, t) and (x,1)1at a later time 1>0. Express Y*...
The particle of mass m in the infinite square well (of width a) starts out of...
The particle of mass m in the infinite square well (of width a) starts out of the left half of the well, and is (at 1-0) equally likely to be found at any point in that region, what is the initial wave function Ψ(0)? Assume it is real, do not forget to normalize it.
5) A particle of mass m is in the ground state of the infinite square well...
5) A particle of mass m is in the ground state of the infinite square well 0 < x < a At t-0 the right hand wall suddenly moves to x = 2a, doubling the size of the well. Assume that this expansion happens on a time scale so fast that the initial wave function (at t0+) is the same as just before the expansion (at t-0-) (This is called the "sudden" approximation.) a) What is the probability that a...
A particle in the infinite square well has as its initial wave function an even mixture...
A particle in the infinite square well has as its initial wave function an even mixture of the first two stationary states: psi(x, 0) = A[psi_1 (x) + psi_2(x)]. Normalize psi(x, 0) (that is, find A). Find psi (x) and |psi (x, )|^2. Express the latter as a sinusoidal function of time. To simplify the result, let omega = pi^2 h/2ma^2. Compute < x >? Compute < p >? If you measured the energy of this particle, what values might...
A particle of mass m is subject to a doubly infinite square well, with widths L,...
A particle of mass m is subject to a doubly infinite square well, with widths L, located at (a/2, a/2). The eigenstate wave functions for this are v(x, y) = L, = a and centre %3D %3D sin () sin ("). nyTy a) Find an expression for the position operator in bra-ket notation. b) Find an expression for the momentum operator in bra-ket notation. c) The particle is initially in the state |) : for position and momentum to find...
please explain all, thanks! 4. (60 pts) A particle in an infinite square well of width...
please explain all, thanks!
4. (60 pts) A particle in an infinite square well of width L has an initial wave function (x,t = 0) = Ax(L - x)2, OSX SL a) Find y(x, t) fort > 0. You first have to normalize the wave function. Hint: this is best expressed an infinite series: show that the wave function coefficients are on = * 31% (12 – n?)(1-(-1)") → (n = 87315 (12 - nºre?); n odd. b) Which energy...
A NON stationary state A particle of mass m is in an infinite square well potential of width L, a...
A NON stationary state A particle of mass m is in an infinite square well potential of width L, as in McIntyre's section 5.4. Suppose we have an initial state vector lv(t -0) results from Mclntrye without re-deriving them, and you may use a computer for your math as long as you include your code in your solution A(3E1) 4iE2)). You may use E. (4 pts) Use a computer to plot this probability density at 4 times: t 0, t2...
A particle in an infinite square well has the initial wave function: (x,0)- A sin(x/a) (0...
A particle in an infinite square well has the initial wave function: (x,0)- A sin(x/a) (0 S a (a) (b) Determine A Find$(z,t) (Hint: You will need to break up this wavefunction into a superposition of pure states. Use orthogonality to find the coefficients.) (c) Calculate (x). Is it a function of time? (d) Calculate (H).
4) A particle in an infinite square well 0 for 0
4) A particle in an infinite square well 0 for 0
1. Consider a particle of mass m in an infinite square well with potential energy 0...
1. Consider a particle of mass m in an infinite square well with potential energy 0 for 0 Sz S a oo otherwise V (x) For simplicity, we may take the 'universe' here to be the region of 0 S z S a, which is where the wave function is nontrivial. Consequently, we may express stationary state n as where En is the associated mechanical energy. It can be shown that () a/2 and (p:)0 for stationary state n. (a)...
2. A particle of mass m in the infinite square well of width a at time 1 - 0 has wave function that is an equal weight mixture of the two lowest n= 1,2 energy stationary states: (x,0) - C[4,(x)+42(x)] (a) Normalize the wave function. Hints: 1. Exploit the orthonormality of W, 2. Recall that if a wave function is normalized at t = 0, it stays normalized. (b) Find '(x, t) and (x,1)1at a later time 1>0. Express Y*...
The particle of mass m in the infinite square well (of width a) starts out of the left half of the well, and is (at 1-0) equally likely to be found at any point in that region, what is the initial wave function Ψ(0)? Assume it is real, do not forget to normalize it.
5) A particle of mass m is in the ground state of the infinite square well 0 < x < a At t-0 the right hand wall suddenly moves to x = 2a, doubling the size of the well. Assume that this expansion happens on a time scale so fast that the initial wave function (at t0+) is the same as just before the expansion (at t-0-) (This is called the "sudden" approximation.) a) What is the probability that a...
A particle in the infinite square well has as its initial wave function an even mixture of the first two stationary states: psi(x, 0) = A[psi_1 (x) + psi_2(x)]. Normalize psi(x, 0) (that is, find A). Find psi (x) and |psi (x, )|^2. Express the latter as a sinusoidal function of time. To simplify the result, let omega = pi^2 h/2ma^2. Compute < x >? Compute < p >? If you measured the energy of this particle, what values might...
A particle of mass m is subject to a doubly infinite square well, with widths L, located at (a/2, a/2). The eigenstate wave functions for this are v(x, y) = L, = a and centre %3D %3D sin () sin ("). nyTy a) Find an expression for the position operator in bra-ket notation. b) Find an expression for the momentum operator in bra-ket notation. c) The particle is initially in the state |) : for position and momentum to find...
please explain all, thanks!
4. (60 pts) A particle in an infinite square well of width L has an initial wave function (x,t = 0) = Ax(L - x)2, OSX SL a) Find y(x, t) fort > 0. You first have to normalize the wave function. Hint: this is best expressed an infinite series: show that the wave function coefficients are on = * 31% (12 – n?)(1-(-1)") → (n = 87315 (12 - nºre?); n odd. b) Which energy...
A NON stationary state A particle of mass m is in an infinite square well potential of width L, as in McIntyre's section 5.4. Suppose we have an initial state vector lv(t -0) results from Mclntrye without re-deriving them, and you may use a computer for your math as long as you include your code in your solution A(3E1) 4iE2)). You may use E. (4 pts) Use a computer to plot this probability density at 4 times: t 0, t2...
A particle in an infinite square well has the initial wave function: (x,0)- A sin(x/a) (0 S a (a) (b) Determine A Find$(z,t) (Hint: You will need to break up this wavefunction into a superposition of pure states. Use orthogonality to find the coefficients.) (c) Calculate (x). Is it a function of time? (d) Calculate (H).
4) A particle in an infinite square well 0 for 0
1. Consider a particle of mass m in an infinite square well with potential energy 0 for 0 Sz S a oo otherwise V (x) For simplicity, we may take the 'universe' here to be the region of 0 S z S a, which is where the wave function is nontrivial. Consequently, we may express stationary state n as where En is the associated mechanical energy. It can be shown that () a/2 and (p:)0 for stationary state n. (a)...
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