The following diagram shows the potential energy function for a harmonic oscillator: (a) (c) (d) (e) (f) U(x) W where U(

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The Following Diagram Shows The Potential Energy Function For A Harmonic Oscillator A C D E F U X W Where U 1 (186.93 KiB) Viewed 28 times

The following diagram shows the potential energy function for a harmonic oscillator: (a) (c) (d) (e) (f) U(x) W where U(x) = bx² and b is a real constant. Write down the time independent Schrödinger equation, TISE, that applies to the harmonic oscillator with this form of the potential. (b) Show that the following wavefunction is a suitable solution to the TISE: 4₁(x) = C₁e-αx² where C₁ is a normalization constant and a is real. Find an expression for the energy E in terms of a and other constants. Find an expression for a in terms of b and other constants. Does this wavefunction have even or odd parity? Explain briefly. Find the normalization condition for this wavefunction. You may find the following information useful: xne-ax² dx = 0 for nodd ∞ FLYIOURNE x2m e-ax² dx = 1.3.5... . (2m - 1) 2m am STA