Recent content by zhaiyujia

  1. Z

    What Condition Determines Eigenket of A?

    But what is the condition? if my first part is right: A(|\alpha>+|\beta>)=a(|\alpha>+|\beta>) is automatic right?
  2. Z

    What Condition Determines Eigenket of A?

    Homework Statement Suppose that |\alpha> and |\beta> are eigenkets(eigenfunctions) of a hermitian operator A. Under what condition can we conclude that |\alpha> + |\beta> is also an eigenket of A? Homework Equations It's quite basic, I don't think any addtional equations are needed except...
  3. Z

    Is \(\psi(x) = \frac{1}{x^{\alpha}}\) in Hilbert Space?

    Thanks, I explained it in the interval of minus infinite to minus zero and zero to infinite. I guess a wave function with singularity is not a good one in physic...
  4. Z

    Is \(\psi(x) = \frac{1}{x^{\alpha}}\) in Hilbert Space?

    one is alpha and another is a. I just write a integral equation, a = 2*alpha. I think it is not the key point. The question is complete. I asked my professor if there is some constrain of x, she said x can be any value. that is to say the integral will from minus infinite to infinite
  5. Z

    Position Operator: f(\hat{x})=f(x)? Effects on g(x)

    is it true that: f(\hat{x})=f(x)? What will happen if f(\hat{x})=\frac{\hat{x}}{\hat{x}+1} act on g(x)?
  6. Z

    Is \(\psi(x) = \frac{1}{x^{\alpha}}\) in Hilbert Space?

    [SOLVED] Hilbert Space Homework Statement For What Values of \psi(x)=\frac{1}{x^{\alpha}} belong in a Hilbert Sapce?Homework Equations \int x^{a}=\frac{1}{a+1} x^{a+1} The Attempt at a Solution I tried to use the condition that function in Hilbert space should satisfy: \int\psi^{2}=A but it...
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