Introduction to Quantum Mechanics · Problem 2.41

Time-Independent Schrödinger Equation — David J. Griffiths

Physics — Quantum Mechanics · half_harmonic_oscillator

Problem

Find the allowed energies of the half harmonic oscillator V(x)={(1/2) mω2x2,x>0,∞,x<0.V(x) = \begin{cases} (1/2)\,m\omega^2 x^2, & x > 0, \\ \infty, & x < 0. \end{cases} (This represents, for example, a spring that can be stretched, but not compressed.) Hint: This requires some careful thought, but very little actual calculation.

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