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**الفيزيائية شيما** · 05-09-2011 04:23 PM

السلام عليكم ورحمة الله وبركاته
ممكن تساعدوني في حل هذة الأسئلة!!
مع شكري وتقديري لكم مقدماً,,,,
.ExternalClass .ecxhmmessage P{padding:0px;}.ExternalClass body.ecxhmmessage{font-size:10pt;font-family:Tahoma;}http://www.nhn.ou.edu/~jeffery/course/c_quantum/problem.pdf

A Particle at energy E>0 approach a potential step from +∞ described by ( 1

>=0V(x) ={v̥for x<0 ,,, 0 for x

Where V0 >0 determine the transmission coefficient and reflection for scattering at the potential step.

A Particle has a wave function ψ(x) =Ce- ^x/a for x>=0 and ψ(x)=0 for x <= 0 Determine (a) the normazation constant C and (b) the avarge value of the position x.(c) where is the probility density p(x)amaximum?

Hent :A useful definite integral is

1. In quantum mechanics, the infinite square well can be regarded as the prototype of:
a) all bound systems. b) all unbound systems.
c) both bound and unbound systems. d) neither bound nor unbound systems.

e) Prometheus unbound.

2. In the infinite square well problem, the wave function and its first spatial derivative are:
a) both continuous at the boundaries.
b) continuous and discontinuous at the boundaries, respectively.
c) both discontinuous at the boundaries.
d) discontinuous and continuous at the boundaries, respectively.

e) both infinite at the boundaries

Afree particle is:
a) bound. b) unbound. c) both bound and unbound.

d) neither bound nor unbound. e) neither here nor there

**الفيزيائية شيما** · 05-10-2011 08:00 AM

وممكن طلب بسيط كمان
أتمنى تزويدي بجميع القوانين الهامة التي تستخدم في حل أي مسألة في ميكانيكا كم!!

**رجب مصطفى** · 05-11-2011 12:39 AM

السلام عليكم ورحمة الله وبركاته

بالنسبة للسؤال الأول فيحتاج إلى كثير من الوقت لكتابته، وهذا مالا أمتلكه حالياً، ولكنه يوجد في أغلب كتب الكم ...

وللسؤال الثاني ... للدالة الموجية:

$\psi (x)= C e^{-x/a}$

لإيجاد ثابت المعايرة ...

$\int_{-\infty }^{\infty}|\psi (x)|^{2}dx= \int_{-\infty }^{0}|\psi (x)|^{2}dx + \int_{0}^{\infty}|\psi (x)|^{2}dx=\int_{0}^{\infty}|\psi (x)|^{2}dx$

إذاً ...

$\int_{0}^{\infty}|\psi (x)|^{2}dx=C^{2}\int_{0}^{\infty}e^{-2x/a}dx=C^{2}\left ( \frac{a}{2} \right )=1$

ومنها ...

$C^{2}=\frac{2}{a}\quad \Rightarrow {\color{Magenta} \quad C=\sqrt{\frac{2}{a}}}\quad \Rightarrow \quad {\color{DarkBlue} \psi (x)=\sqrt{\frac{2}{a}}\:\:e^{-x/a}}$

و:

$\left \langle x \right \rangle=\int_{0}^{\infty }x\;|\psi (x)|^{2}\;dx=\left (\frac{2}{a} \right )\int_{0}^{\infty }x\;e^{-2x/a}\;dx$

أو:

$\left \langle x \right \rangle=\left (\frac{2}{a} \right )\left (\frac{a}{2} \right )^{2}\Gamma (2)=\left (\frac{a}{2} \right )$

**رجب مصطفى** · 05-11-2011 12:41 AM

1. In quantum mechanics, the infinite square well can be regarded as the prototype of:
a) all bound systems.
b) all unbound systems.
c) both bound and unbound systems.
d) neither bound nor unbound systems.
e) Prometheus unbound.

2. In the infinite square well problem, the wave function and its first spatial derivative are:
a) both continuous at the boundaries.
b) continuous and discontinuous at the boundaries, respectively.
c) both discontinuous at the boundaries.
d) discontinuous and continuous at the boundaries, respectively.
e) both infinite at the boundaries

3. A free particle is:
a) bound.
b) unbound.
c) both bound and unbound.
d) neither bound nor unbound.
e) neither here nor there

والله أعلى وأعلم