MY-ASSIGNMENTEXPERT™可以为您提供catalog.winona.edu PHYS451 Quantum mechanics量子力学课程的代写代考和辅导服务！
这是华盛顿州立大学量子力学课程的代写成功案例。
PHYS451课程简介
Prerequisites, PHYS 250 and PHYS 201 or PHYS 207. Students learn the basic principles of quantum mechanics, which describe atomic, molecular, and nuclear physics. Students learn general concepts, methods, analytic tools and advanced problem-solving skills. Topics include evidence for and origins of quantum mechanics, mathematical background, the postulates of quantum mechanics, one-dimensional systems, quantization of angular momentum, and three-dimensional quantum systems including the hydrogen atom. Letter grade with Pass/No Pass option. (Offered fall semester.) 3 credit
Prerequisites
In this course, students learn the basics of non-relativistic quantum mechanics. The course introduces the concept of the wave function, its interpretation, and covers the topics of potential wells, potential barriers, quantum harmonic oscillator, and the hydrogen atom. Next, a more formal approach to quantum mechanics is taken by introducing the postulates of quantum mechanics, quantum operators, Hilbert spaces, Heisenberg uncertainty principle, and time evolution. The course ends with topics covering the addition of angular momenta, spin, and some basic aspects of many-body quantum mechanics. The course will include two lectures per week accompanied by a recitation.
PHYS451 Quantum mechanics HELP（EXAM HELP， ONLINE TUTOR）
Consider the wavepacket:
$$
\psi(x)=A \exp \left[i k_0 x-\frac{\left(x-x_0\right)^2}{4 \sigma^2}\right],
$$
where $A, k_0, x_0$, and $\sigma$ are some real constants.
(a) Determine the normalization factor, $A$.
(b) Find the wave function in the momentum space, $\psi(k)$.
(c) Calculate $\langle x\rangle,\left\langle x^2\right\rangle$, and $\Delta x$.
(d) Calculate $\langle p\rangle,\left\langle p^2\right\rangle$, and $\Delta p$.
(e) Calculate the probability current, $j(x)$
Demonstrate that
$$
\delta(x)=\lim {\epsilon \rightarrow 0^{+}} \frac{1}{\pi} \frac{\epsilon}{x^2+\epsilon^2} $$ is a valid representation of the Dirac delta function. Namely, show that (a) $\int{-\infty}^{+\infty} \delta(x) f(x) d x=f(0)$ for any reasonably “nice” function $f(x)$.
(b) $\delta(x)=\delta(-x)$
(c) $x \delta(x)=0$.
(d) $\delta(c x)=\frac{1}{|c|} \delta(x)$
(e) $\delta^{\prime}(-x)=-\delta^{\prime}(x)$
(f) $x \delta^{\prime}(x)=-\delta(x)$
Consider the wavepacket:
$$
\psi(x)=A \exp \left[i k_0 x-\frac{\left(x-x_0\right)^2}{4 \sigma^2}\right]
$$
where $A, k_0, x_0$, and $\sigma$ are some real constants.
(a) Determine the normalization factor, $A$.
(b) Find the wave function in the momentum space, $\psi(k)$.
(c) Calculate $\langle x\rangle,\left\langle x^2\right\rangle$, and $\Delta x$.
(d) Calculate $\langle p\rangle,\left\langle p^2\right\rangle$, and $\Delta p$.
(e) Calculate the probability current, $j(x)$
Consider the following operators and determine whether they are linear or not:
(a) Multiplication operator, $\hat{M}_a: \quad \hat{M}_a f(x)=a f(x) \quad(a$ is a constant $)$
(b) Exponentiation operator, $\hat{E}: \quad \hat{E} f(x)=e^{f(x)}$
(c) Differentiation operator, $\hat{D}_x: \quad \hat{D}_x f(x)=\frac{\partial f(x)}{\partial x}$
(d) Integration operator, $\hat{S}_x: \quad \hat{S}_x f(x)=\int_0^x f\left(x^{\prime}\right) d x^{\prime}$
(e) Addition operator, $\hat{A}_a: \quad \hat{A}_a f(x)=f(x)+a \quad$ ( $a$ is a constant)
(f) Translation operator, $\hat{T}_a: \quad \hat{T}_a f(x)=f(x+a) \quad$ ( $a$ is a constant)
(g) Inversion operator, $\hat{I}: \quad \hat{I} f(x)=f(-x)$
(h) Complex conjugation operator, $\hat{C}: \quad \hat{C} f(x)=f^*(x)$
(i) Operator that projects out the odd part, $\hat{O}: \quad \hat{O} f(x)=\frac{1}{2}[f(x)-f(-x)]$
(j) Operator that computes the absolute value, $\hat{N}: \quad \hat{N} f(x)=|f(x)|$
(k) Operator that squares the argument, $\hat{Q}: \quad \hat{Q} f(x)=f\left(x^2\right)$
Consider a particle that moves in $1 \mathrm{D}$ with Hamiltonian $\hat{H}=\frac{p^2}{2 m}+V(x)$. Show that the uncertainties of $\Delta p_x$ and $\Delta E$ obey the following inequality:
$$
\Delta p_x \Delta E \geq \frac{\hbar}{2}\left|\left\langle\frac{\partial V}{\partial x}\right\rangle\right| \text {. }
$$
What does it imply for stationary states?
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