一个粒子的两种状态分别具有能量E1和E2，并且以下两个正交的，已经归一化的函数(f1,f2)是薛定谔方程的解 f1(x，t)=f1(x，t)*exp(-i*(E1*t/h)),f2(x，t)=f2(x，t)*exp(-i*(E1*t/h))
a) 求f1和f2的线性叠加态，这个线性叠加态的能量期望(expectation value of the energy)为0.25*E1+0.75*E2
b) 求这个线性叠加态中能量的不确定度(uncertainty energy)
c) 求这个叠加态中，概率密度随时间的变化，谐振，并找出谐振子周期和能量的不确定度的关系。
这题是我翻译过来的，如果有些名词不太对，请看下面英文原题
Two states of a particle with definite energy E1 and E2 are represented by the following normalized, orthogonal solutions of the Schrödinger equation:
f1(x，t)=f1(x，t)*exp(-i*(E1*t/h)),f2(x，t)=f2(x，t)*exp(-i*(E1*t/h))
a) write down a linear superposition of f1 and f2 which represents the state for which the expectation value of the energy is 0.25*E1+0.75*E2.
b) find the uncertainty in energy for the state written down.
c)show, for the state written down, that the probability density oscillates with time. find the relationship between the period of these oscilations and the uncertainty in the energy.
a) 求f1和f2的线性叠加态，这个线性叠加态的能量期望(expectation value of the energy)为0.25*E1+0.75*E2
b) 求这个线性叠加态中能量的不确定度(uncertainty energy)
c) 求这个叠加态中，概率密度随时间的变化，谐振，并找出谐振子周期和能量的不确定度的关系。
这题是我翻译过来的，如果有些名词不太对，请看下面英文原题
Two states of a particle with definite energy E1 and E2 are represented by the following normalized, orthogonal solutions of the Schrödinger equation:
f1(x，t)=f1(x，t)*exp(-i*(E1*t/h)),f2(x，t)=f2(x，t)*exp(-i*(E1*t/h))
a) write down a linear superposition of f1 and f2 which represents the state for which the expectation value of the energy is 0.25*E1+0.75*E2.
b) find the uncertainty in energy for the state written down.
c)show, for the state written down, that the probability density oscillates with time. find the relationship between the period of these oscilations and the uncertainty in the energy.
