Specifying Node Matrices

• In the Node Prior-Info. window, make root  the focus node. Note that since root  has no incoming arrows, its list of parent nodes is empty. In the Amplitudes box:
  • In the row of state (0,1), insert 0.5 for the Real Part and 0.5 for the Imaginary Part.
  • In the row of state (1,0), insert 0.707107 (i.e. 1/sqrt(2)) for the Real Part.
  • All other entries of the Real and Imaginary Part columns should remain at their default values of zero.
• Make nz+  the focus node.
  • For 1mag  = (0,0) in the Parent Nodes box, make the following changes in the Amplitudes box. In the row of state 0, set the Real Part to 1.

    Explanation of last action: We are using the notation (n-, n+) to represent a state of 1mag , where n- is the number of spin - particles and n+ is the number of spin + particles. Node nz+  has 2 states, 0 and 1, where the numbers 0 and 1 tell how many particles of spin + go through node nz+  . By setting to 1 the amplitude of nz+  =0 when 1mag  = (0,0), what we are saying is that with unit amplitude, when 1mag  =(0,0), zero particles of spin + traverse node nz+  .

  • For 1mag  = (1,0) in the Parent Nodes box, make the following changes in the Amplitudes box. In the row of state 0, set the Real Part to 1.
  • For 1mag  = (0,1) in the Parent Nodes box, make the following changes in the Amplitudes box. In the row of state 1, set the Real Part to 1.
• Make nu+  the focus node.
  • For 2mag  = (0,0) in the Parent Nodes box, make the following changes in the Amplitudes box. In the row of state 0, set the Real Part to 1.
  • For 2mag  =(1,0) in the Parent Nodes box, make the following changes in the Amplitudes box. In the row of state 0, set the Real Part to 1.
  • For 2mag  =(0,1) in the Parent Nodes box, make the following changes in the Amplitudes box. In the row of state 1, set the Real Part to 1.
• Make nz-  the focus node.
  • For 1mag  = (0,0) in the Parent Nodes box, make the following changes in the Amplitudes box. In the row of state 0, set the Real Part to 1.
  • For 1mag  = (1,0) in the Parent Nodes box, make the following changes in the Amplitudes box. In the row of state 1, set the Real Part to 1.
  • For 1mag  = (0,1) in the Parent Nodes box, make the following changes in the Amplitudes box. In the row of state 0, set the Real Part to 1.
• Make nu-  the focus node.
  • For 2mag  =(0,0) in the Parent Nodes box, make the following changes in the Amplitudes box. In the row of state 0, set the Real Part to 1.
  • For 2mag  =(1,0) in the Parent Nodes box, make the following changes in the Amplitudes box. In the row of state 1, set the Real Part to 1.
  • For 2mag  =(0,1) in the Parent Nodes box, make the following changes in the Amplitudes box. In the row of state 0, set the Real Part to 1.
• Make 1mag  the focus node. Press the Generate Amplitudes... button at the bottom-right corner of the Node Prior-Info. window. A window entitled "Parameters Of Stern-Gerlach Magnet" will open.
  • The Theta and Phi boxes at the top allow you to specify the polar coordinates of the magnetic field of the Stern-Gerlach Magnet. Set Theta and Phi to zero (their default value), indicating that the magnetic field points in the + Z direction.
  • The Theta and Phi entries of the table allow you to specify the direction of the spin axis for the particles coming from root  . Set both of these angles to zero (their default value), indicating that the particles emanating from root  are polarized along the Z direction.

    Press the OK button. Now scan over the 3 possible input states of 1mag  by pressing successively the Next button of the Parent Nodes box. You'll see that the Amplitudes box contains new amplitudes for each of the input states.

• Make 2mag  the focus node. Press the Generate Amplitudes... button at the bottom-right corner of the Node Prior-Info. window. A window entitled "Parameters Of Stern-Gerlach Magnet" will open.
  • The Theta and Phi boxes at the top allow you to specify the polar coordinates of the magnetic field of the Stern-Gerlach Magnet. Set Theta to 36 degrees and Phi to zero degrees.
  • The first row of the bottom table shows that nz+  is a Parent Node. Click on the Spin entry of this row until it reads +. Set both Theta and Phi of this row to zero degrees.
  • The second row of the bottom table shows that nz-  is a Parent Node. Click on the Spin entry of this row until it reads -. Set both Theta and Phi of this row to zero degrees.

  Press the OK button. Now scan over the 4 possible input states of 2mag  by pressing successively the Next button of the Parent Nodes box. You'll see that the Amplitudes box contains new amplitudes for each of the input states.

• Save your work by selecting the Save item of the File menu.

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