Read More
Date: 14-8-2016
1005
Date: 30-8-2016
1078
Date: 19-8-2016
1137
|
Time-Dependent Harmonic Oscillator I
Consider a simple harmonic oscillator in one dimension:
(i)
At t = 0 the wave function is
(ii)
where ψn (x) is the exact eigenstate of the harmonic oscillator with eigenvalue hω(n+1/2).
a) Give Ψ(x, t) for t ≥ 0.
b) What is the parity of this state? Does it change with time?
c) What is the average value of the energy for this state? Does it change with time?
SOLUTION
a) At times t ≥ 0 the wave function is
(1)
b) The state Ψ(x, t) has even parity: it remains the same if one replaces x by –x, since ѱ2n(-x) = ѱ2n(x). This is true for all times.
c) The average value of the energy is
(2)
which is independent of time.
|
|
كيف تساهم الأطعمة فائقة المعالجة في تفاقم مرض يصيب الأمعاء؟
|
|
|
|
|
مشروع ضخم لإنتاج الهيدروجين الأخضر يواجه تأخيرًا جديدًا
|
|
|
|
|
المجمع العلمي يختتم دورته القرآنية في فن الصوت والنغم بالطريقة المصرية
|
|
|